From the engines I can advise: AndEngine , LibGDX will go fine for a simple 2D game. Cocos2d-Android-1 did not like me. If interested, I will describe separately why. What they offered above is paid and very sophisticated, and there are many nuances here. I doubt that it is worth starting with them, especially if there is no experience in game development or a precise plan, the game will take off and as the most important thing.
Also, you need to learn OpenGL ES (a subset of OpenGL) and related math. It helps to understand.
Games test better on devices with popular resolutions themselves. Itself faced such problem not so long ago. On the emulator, for example, you have to set the emulation of an accelerometer or something else
You should start by installing Eclipse + plugins for Android from Google and your friend is developer.android.com. There is everything you need to learn the basics and a lot of sample applications, although they are also in the SDK you installed (assuming that the corresponding check mark). In addition, a bunch of examples can be found in Google.