Develop Reference

What is the difference between Google Developers Console project and a Google **Play** Developers Console project?

I have removed my Google Developer Console project.
Are these projects identical to each other? If I remove one, will it remove the other?

Difference between Google Developers Console and a Google Play Developers Console?
Google Developers Console: Google Developers (previously Google Code) is Google's site for software development tools, application programming interfaces (APIs), and technical resources. The site contains documentation on using Google developer tools and APIs—including discussion groups and blogs for developers using Google's developer products.
Google Play Developers Console:
Google Play or Google Play Store, and originally the Android Market, is a digital distribution platform operated by Google. It serves as the official app store for the Android operating system, allowing users to browse and download applications developed with the Android SDK and published through Google. Google Play also serves as a digital media store, offering music, magazines, books, movies, and television programs.
Answer of your Question
No, If you remove your project from Developers Console it will not delete your Application from Google Play Store, but the funcationality witch is working due to your Google Developers Console project stops and your Application will not work as it was previously.
Note: Your Project will be permanently deleted from Google Developers Console after 7 days when you deleted it. You can restore your project in the mean time.

The Google Developer Console is a place where you can register your applications for using any of the Google APIs (example: Google plus) or using the Google infrastructures.
The Google Play Developer Console is where you upload your Android App, publish, view statistics, etc.
Removing your project from one will not remove it from the other.

Is there a way to download Google Play Services SDK R15?

Is the Google Play Services SDK R15 available to download anywhere? The "ChromeCast SDK" was "released" Monday, according to hundreds of news sites. Those same news sites claim Android app developers are "hard at work implementing ChromeCast functionality." Is the SDK appearing in anyone's SDK Manager?
How are Android app developers implementing ChromeCast functionality when the SDK isn't available and the API has changed dramatically? The DayFrame developers supposedly already updated their app to the new API, which seems suspicious to me...

Edit - As per the announcement post, SDK15 is now available.
As per the Chromecast Android API reference:
These APIs are currently not available for development. They require Google Play services 4.2, which began rolling out to devices worldwide on February 3rd. Once the update to devices is complete, the corresponding Google Play services library (revision 15) will be available for you to begin using these APIs.
Certain developers have been given early access to the SDK directly from Google to allow early development, but general availability of SDK R15 is still to come. You can still read through the Developers Guide and the Android Sender App Development Guide and prepare your application, design, and resources appropriately, but the actually integration of the SDK and testing cannot occur until Google releases it officially after the full rollout of Google Play Services 4.2.

Google Play Services error in android emulator (eclipse)

Hey I've been trying since a week now to get the maps thing working on Eclipse. I downloaded all the necessary packages and did everything that they've asked to on the "getting started" page on google's developer site that is meant for developing using Google Maps. But when I run the code in the emulator it tells me, "Google play services is not supported by your device"
Need some help guys as to what to do. Please do let me know about any suggestions.

Yup, you can get Google map V2 in emulator too. I got it please refer this step by step procedure this link which I answered in previous question.

To work with Google Map API v2, you are required to have Google Play services enabled device.
To test your app when using the Google Play services SDK, you must use either:
A compatible Android device that runs Android 2.3 or higher and includes Google Play Store.
The Android emulator with an AVD that runs the Google APIs platform based on Android 4.2.2 or higher.
Update:
I would suggest you to give Genymotion emulator a try.

Google Plus Android API : "This app won't run unless you update Google Play Services"

I am playing with the Google sample app relative to the Google Plus SDK (sample app provided by Google here: https://developers.google.com/+/quickstart/android)
I can run the sample app. But when I want to login to Google Plus from within the app, I get the message: "This app won't run unless you update Google Play Services". If I click on the update button, I see that I have got the last update of the Google Play Services (v3.2.66). In Eclipse, I have got rev. 13 of Google Plus SDK.
How can I solve this problem?

This was a bug in the Google+ app that is fixed in the latest build that came out today: https://plus.google.com/101870761930221849874/posts/KohXe9pBGF6 Sorry about that.

Google plus in android app

I am working on an app with integration for facebook, twitter, flicker, and Google plus. I have done all the things besides Google plus.
Has anyone used Google plus API in his own app?

The Google+ Platform for Android is now available.
With the platform, you are able to:
Allow users to sign in with Google+.
Integrate the native +1 button.
Write moments to the user's Google+ history (developer preview)
For more information, see:
https://developers.google.com/+/mobile/android/

Right now there is no official API for Google Plus for Android. Check out the official documentation here.
Quote:
The Google+ platform for Android will soon be available in the coming
weeks — this documentation gives you a quick overview of what to
expect.