I read the information about the engines, but I would like to know, mainly on what many games for Android are created (2d, 3d, logical, etc.), is it possible to create all this in Eclipse, for example?
You can, for example, using AndEngine:
AndEngine is an engine for writing 2D games for Android. The engine is free, productive. It has a large set of functions: working with sprites, built-in controls, on-screen joysticks, physics module, support for working with sound, text, menus, etc.
By Nicolas Gramlich. Project page in Google Game from the author of the Farm Tower engine - 2d puzzle, uses the physics library in the calculations.
There is practically no documentation for it, which is typical of many free development projects. Ways to work with him are passed on from mouth to mouth or on gourmet forums. The lack of documentation is compensated by the presence of many simple examples of using the functions of the engine.
The engine is installed on IDE Eclipce.
The main engines are AndEngine and libgdx. Both 2d and both are free. The first is a little more brake (as they say, I did not check it myself). Both are quite simple to use. From paid you can select Unity 3d (available for Android).
In general, enter the query in google "android game engines" and get a lot of information.
It is worth adding that the engines - this is certainly great, but you need to know the mat.part and OpenGL. The engines just slightly simplify the work with OpenGL, realizing the frequent things in the game. But without fundamentals, something serious is meaningless.
And you can (and should) write a graphical part in C ++ from the Android NDK (Cocos 2dx engine using for example) and then you will have a cross-platform part that can be separated from the platform (ios, android, bada) and quickly ported to other OS.
To write games for Android, you first need to know the Java language well. And in Eclipce is not possible, but you need to work. Just for this, you need to install an add-on in Eclipce, called the Android SDK, and install the JDK extension package ( Java Development kit )