Swipe/drag Android view from the bottom of the screen

You can use the new material design pattern called Bottom Sheets. They do the exact thing that you want. They also support custom layouts for the view.

Material Design - Component - Bottom Sheets

I think you are in search of a ViewDragHelper:

API doc: https://developer.android.com/reference/android/support/v4/widget/ViewDragHelper.html

How to use. This answer links to a sample project to show you how as well: ViewDragHelper: how to use it?

Dragging best practices:

http://developer.android.com/training/gestures/scale.html