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Create full mobile app vs Create app that goes to a server which handles mobile

I have been playing around with PhoneGap for a little while, and getting it set up to work correctly with Google Drive API is proving to be far more difficult than setting up a website which does the same.
I am wondering if it would be more to my advantage to cease trying to make the full app work with phonegap, and instead use phonegap to access a hosted site.
Note that I do not wish to open the site in the default browser. The goal would be to make it appear to be an application (no borders, url, back button, etc), but have the web server handle everything behind the scenes.
I know PhoneGap has an In-App-Browser available. Is this something that is possible with it? Or does it only function for more limited use?
Thanks

You can definitely use a WebView for your app, which display the webpage but give you the ability to control the layout around it. Running a WebView instead of native code may cost some performance but it's doable.

What is the correct way developing website applications in Cordova?

I'm trying to do some simple website application for displaying my website and add some specific functionality to it.
My idea is to do something like Facebook app for mobile. Simply I need to display a website and replace File input - users should be able to capture a picture from camera or pick it from gallery (multiple select) and attach it to a post.
TL;DR;
Check images in the bottom.
What I have tried:
Using Cordova with Camera and Image picker plugin and displaying webpage in InnAppBrowser
Taking pictures with camera and picking pictures from gallery and then uploading them to server - there is a lot of examples of it.
What troubles I have found:
InnAppBrowser is forced fullscreen so I cannot resize it and place some buttons for picking pictures under it.
What do I need:
I just need to somehow attach images (from gallery or camera) to form file input or upload them to some kind of api instead - the api would process images on server and return some IDs which I can use instead of file input in the form on page to attach images to the post. Some hidden input where I would just insert IDs of uploaded images to be attached to the post (I'd write some if conditions into my PHP script).
I need my application to be multi-platform (Android, IOS, WP) so that is the reason I'm using Apache Cordova. I've tried lot of solutions and I've searched like for 5 hours. But I wasn't able to find anything useful.
Have somebody some experience in this way? Did somebody make some kind of that application?
If you can suggest any solution (it is not important to be a Cordova but it must be multiplatform) I'd be glad!
Thanks for your time!
Images
There is screen of desktop version with normal file input:
There is my vision of mobile application version with camera and image picker option right under web browser:

I guess I was not clear. The technical answer is Cordova/Phonegap are not for creating website applications. This means technically there is no "correct way" to do what you are asking.
For a website applications, all the pages are rendered from the website and controlled from the webpage/webbrowser.
For a mobile application, all the pages that the application can directly control are rendered on the mobile device. However, pages can be rendered (and/or created) from either the server or the mobile application, but the control of the page stays with the side that rendered (or created) the page. There is clear line between the two sides that can be moved, but at the *peril* of the programmer. (There are no points for being clever here, only added security issues.)
However, the Cordova and Phonegap do have plugins.The entire purpose is to use plugins to make certain task easier. However, there is a clear line between the phone and the website. To be clear on this last part, this means that all of the "plugin services" on the phone (accelerometer, contact list, etc.) are directly available to the application, and not the website. However, some of the "services" are also available as HTML5 APIs, such 'camera' and 'geolocation' – mixing the two is dangerous. The HTML5 APIs should remain on the webserver side, if used. The UX is different for HTML5. (I will not discuss HTML5 APIs any further, as they are beyond the scope of this discussion)
To make your idea work, you will need the following "core" (or equivalent third-party) plugins
file-transfer
camera (or equivalent)
inappbrowser
On the file-transfer and camera, you can do everything from the webserver, if you want. Then the only task for the end-user is to select the appropriate folder and image. If you do this from the server-side, then you CANNOT use the plugins.
If you want to use the plugins, then you cannot use a server-side generated webpage. You must create the form on the mobile device. This means the page and the form reside on the mobile device. However, if you write your webpage correctly you can dynamically add or delete elements. This means on the mobile side you have control over every step of the user experience and can enhance that experience.
On the inappbrowser, a common trick is to put the website in an iframe. However, you have no direct control on the iframe. Another common trick is to submit to the server via an API – then have the visible webpage update separately. Another common trick is to have a webpage with a websocket that could handle the webpage update. However, this could also be done with a push to the webpage, or have the webpage do polling of the server. Again, the App has NO direct control of the webpage.
This entire thread makes the following assumptions.
There is no "correct way" to do this task.
The images (photos) are stored on a website, and are publicly available for viewing.
It also assumes that no HTML5 APIs will be used.

If I interpreted your problem statement correctly, I believe what you are looking for is access to device native services - camera & gallery - from your mobile website.
A solution that fits your design requirements is for the browser to provide such services. Unfortunately WebKit and other browsers limit such support to things like Geoposition.
The way for Cordova to help you here is if your mobile website is an stand alone HTML5/CSS/JS application that can use CORS XHR or WebSockets to communicate with webindependent Web Services.
If you can bottle your website into a set of static html/js/css files that display content from dynamic web services then you are set. That same javascript can then call navigator.camera.getPicture(success, fail, options) and file-transfer the result to a waiting web service.
That camera api is not available to the InAppBrowser just as it is not available to WebKit Chrome/Safari/Edge. Trying to control the Mobile App via the InAppBrowser is most likely to fail due to security constraints.
What you might get away with is re-imaging your browser application as a series of discrete services that return raw html snippets suited for a new mobile app. Then write your Cordova app as the top level container that manages the navigation amongst the html snippets. This server-side rendering would be most useful if it was significantly challenging enough to overwhelm the mobile platform / web services pattern (think custom video server or expert system).

#Jakub,
Cedric has essentially stated it plainly. I will restate. You understanding about Cordova/Phonegap is not correct.
From: Top Mistakes by Developers new to Cordova/Phonegap
You have hit issue #5.
I QUOTE:
From Phonegap FAQ
A PhoneGap application may only use HTML, CSS, and JavaScript. However, you can make use of network protocols (XmlHTTPRequest, Web Sockets, etc) to easily communicate with backend services written in any language. This allows your PhoneGap app to remotely access existing business processes while the device is connected to the Internet.
In addition, Apple frowns on using apps as wrappers for websites.
Quote Apple iTunes Guidelines - 2.12
Apps that are not very useful, unique, are simply web sites bundled as Apps, or do not provide any lasting entertainment value may be rejected
To be clear, your idea may be valid, but you will likely need to rethink your internal workflow. You likely want to keep the same UI and UX.

Simple Browser/Website web app mobile app/shortcut

I have a website/web app which I want to make available on mobile devices.
The website is responsive and can be used inthe mobile browser, but I want to make it available on google play / app store. My question is: how could I create a simple app that is actually a browser, which would run natively on the phone but load my web page in full screen?
Any simple solutions or frameworks?

Well there are different approaches to solve your questions I am trying to give you some rough idea with following two approaches.
Easy and simple one
1) Use web views and call home page url that's all.
For better performance.
2) Create a REST apis with only required data for your mobile app . And then use either web view or create your own views and show it to user . In this case if you create your native view then app will perform faster but development will take time.

What is the easiest way to turn a webapp into a mobile app?

The company I work for is exploring creating "an app" version of their online video delivery webapp. The webapp is HTML5 and streams video. Nothing too scary but a lot of the stuff is server-side authentication with third party video hosts, code that will never be in a mobile app for security reasons.
The webapp has a lovely mobile stylesheet that works fine. We want an app that:
Shows a quick splash screen (and even that's optional)
Load the existing mobile website (not include it within the app)
And have the ability to specify an icon, give it a name and then shove it in the relevant marketplaces. That should satisfy the marketing department and it means I stay in control of what the app actually does.
Yeah, it's possibly the laziest app development ever... But, what's the simplest way to generate something like this? I was imagining there might be something out there already where you feed it your starting URL, splash screen, icon and name and it hands you back a multi-platform app.
Note: I'm not looking for something to create an app that looks like the mobile website and I'm not looking to put the content of the mobile website inside the app, I essentially just want a browser that loads the real mobile site.

Have a look at https://www.shoutem.com/. They provide a service similar to what you seem to be looking for but they charge royally for it. Considering the extra features you can easily add with their service your marketing department might just smell profit from using it and may therefore happily sign it off with their well known satanic smile.

There are a number of websites which provide easy web app development for a website. One of the famous is App Maker . Others include:http://www.viziapps.com/ and http://ibuildapp.com/

Since posting this, I have found:
http://www.websitetoapp.net/create
Feed it a URL and an Icon and it'll give you an Android app. Pay $5 and they'll disable adverts. Seems like it might be perfect for the Android half of this project.
Now, is there anything out there that will do this for other platforms?

How do I use webview to embed the web app in a native Android App?

I have a fully-working web app that is accessible using Android's browser.
The annoying part is the url bar uses a lot of the screen. Is there a way to make this web app a native Android app? I've read that webview can be used to embed a web site within the Android App.
Unfortunately, I only know web programming languages and have no Java experience. Will I still be able to do this on my own?

You certainly will need some learning in java, you can start with reading the following :
Webview documentation
A very detailled tutorial (quite hard if you haven't any java basics)
A basic tutorial on webview usage.

Have you looked at phonegap. It comes with a standalone app with a WebView embedded in it and with native android functionality support. You just need to provide your html/javascript app to it and you're done.

You can use a web app called MIT App Inventor
and get it done in less than 10 minutes, it's very easy, intuitive and requires no programming skills at all.
all you need to do is create a new project,
drag and drop a WebViewer component, on the right set the home url,
and your done! just connect to an android phone via USB to install the app
and you can even download the .apk to your computer, sign it and publish it on Google Play