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How do I create an android navigation bar that pushes aside the current view to right?

I need a navigation bar that doesn't slideIn above the current view (the usual overlapping stype), instead it should be as in new ebay app (as if scrolling the wallpaper in homescreen with more than one page). Is it possible to add this effect to material-design-navigation-view? How do I do it?

You can use Sliding Menu Library for your requirement. Here is the link to that library
Sliding Menu Library
And if you are using Android Studio then see this link to add it in your project
Importing in Android Studio

There is no default way to really do this. However, this thread of StackOverflow will help you: push activity on the right when open drawer
Another GitHub library that may suit your need is: Material Drawer. You can download the demo on Google Play Store (same name). A similar approach is the Persistent Header Drawer

Android Navigation Drawer should be centralized vertically

I have made my navigation drawer and it is working all fine , it is according to new design rules. but now I have a problem and after a couple of search I have found no note over it so far. So I end up with asking question here.
What I have done so far is some thing like
the picture shows you the demo , How ever I have made some thing like this its just the demo to give you people hint about what is header in the navigation drawer and where my menu items list lies
You can clearly see that there is a header in the navigation drawer and the menu item list beneath it .
Problem 1
now do to some reasons I have deleted the header , but my menu Items goes upwards to the top starting point. I know I can give margin up , but this is not the good way
Is there any good way I can just centralized them vertically ? I am wondering How to do it , Please Help me .
and Problem 2 is , I want to minimize the distance and margin between the menu items and menu icons in navigation drawer How to do this. I have not seen any of the discussion over it.
Please help me in solving both problems.

On screenshot you attached to your question, the navigation drawer doesn't look fine and according to the new desing rules :-/
Just have a look at the official guide: https://www.google.com/design/spec/patterns/navigation-drawer.html
Luckly for you nowdays we are provided by Google with Android Design Support Library that helps us with creating Navigation View (that replaces Navigation Drawer)
Here are links for you:
official documentation, always a good read: https://developer.android.com/reference/android/support/design/widget/NavigationView.html
nicely written blog post about Navigation View: http://antonioleiva.com/navigation-view/
and last but not least, sample app using new Android Design Library: https://github.com/antoniolg/MaterializeYourApp
I know it's not the answer you were looking for, like "just change true to false in the line number 10" but stay assured that using official Navigation View is a way to go in modern Android world.

You can use the new NavigationView from the Android Design Support Library in making your navigation drawer. NavigationView make s creating material design-compliant navigation drawer.
You can read about it at http://android-developers.blogspot.com/2015/05/android-design-support-library.html

Read these three articles
Take a look at this code
Use the design support library

Best way to make swipe tabs

I've just decided to add swipe views on my android application. I searched for them on the web for tutorials but I found nothing but deprecated actionBar tutorials. Event in official Creating Swipe View from android developer is showing me that this is deprecated method for this purpose. So tell me guys - what's the best way to make a swipe tab view?

I think you can use the templates included with ADT.
Just create new "Android Application Project" and select "tabbed activity" during wizard flow, and select "Navigation Style" = "swipe views" on the last wizard screen.
You can either develop your application on base of code you received, or study it to understand how swipe and tabs are working together.

Action bar tab is now depreciated because of new toolbar facility . You can use now Sliding tab https://developer.android.com/samples/SlidingTabsBasic/src/com.example.android.common/view/SlidingTabLayout.html for creating swipe views using view pager

Use a Sliding tab Layout.
Get the Sliding Tab Layout & Sliding Tab Strip java file in the following link.
https://github.com/google/iosched/tree/master/android/src/main/java/com/google/samples/apps/iosched/ui/widget
Copy the 2 into your project and follow the follwing tutorial.
Note: Dont copy the one in the developers android website its not updated as far as I know
https://www.youtube.com/watch?v=Fl0xMuo10yA&index=26&list=PLonJJ3BVjZW6CtAMbJz1XD8ELUs1KXaTD
I had the same problem.

Sliding Layout in Android

I want to put settings in left side of screen.
There will be switcher, listviews and textviews.
In result I need like this example:
Is it possible and how I can start with?

You can use Sliding Menu Library to give such effect...
You can get the code from here.
You can also refer this link.

It's possible, and you can implement it using the Navigation Drawer which comes with android support library.

You must check out the Ribbon Menu
1) What's the Purpose
Ease of Access: Allow easy access to a menu that slides in and out
Ease of Implementation: Update the same screen using minimal amount of code
Independency: Does not require support libraries such as ActionBarSherlock
Customization: Easy to change colors and menus
2)What's New
Changed the sliding animation to match Facebook and Google+ apps
Added standard ActionBar (you can chose to use ActionBarSherlock)
Used menuitem to open the Menu
Added ability to update ListView on main Activity
Added 2 ListViews to the Menu, similiar to Facebook and Google+ apps
Added a AutoCompleteTextView and a Button as well to show examples of implemenation
Added method to allow users to hit the 'back button' to hide the menu when it is open
Allows users to interact with background(main ListView) and the menu at the same time unlike the Facebook and Google+ apps!
OR
You can also try out with Sliding Menu

You have to add one library file slider.jar into your project and follow this example for the same :
http://www.oodlestechnologies.com/blogs/Facebook-Style-Slide-Menu-In-Android

How to replicate the example navigation drawer from Android Docs?

For example, please view this image from the Android Developers site.
Basically, I want to replicate this navigation drawer, currently I have it all except the sub items (Option 1, Option 2, in the example). There is no documentation on how to get this on the developers site. This is what I have currently:
MainActivity.java: http://pastebin.com/iNXW00ex
SeparatedListAdapter.java: http://pastebin.com/fESuvEVi
MainActivity.xml: http://pastebin.com/gg4JANwh
Drawer Item/Header.xml: http://pastebin.com/WzvPXQYm
That's all I think is needed. I'm aware that typically a expandable list view is used for the child items, though I'm unsure how to combine that with the current separated list adapter so I can still get titles.
Thanks, David.

There are a lot of third party libs for sliding menus.
Why not use one of them instead of trying to recreate Android's?
For example:
https://github.com/jfeinstein10/SlidingMenu

Have you checked out the Navigation Drawer tutorial in the Android docs?
http://developer.android.com/training/implementing-navigation/nav-drawer.html
Uses classes in the support library to make implementing the nav drawer pretty straightforward.