After Effects

Without any system information and other details about your settings for hardware acceleration, caches, memory and all that we cannot tell you why the program goes unresponsive.

Mylenium 

Heya, @18187696 

Were you looking for some tips on how to use After Effeets or just looking to vent frustration? 

It does have a bit of a steep learning curve.

Compositions are part of a Project, hence the need to have a Project open in order to animated.

The "New Composition" and "New Composition from Footage" options only appear where a Composition goes to get things started.

What you described is done by dragging a Composition onto the "Create a New Composition" button at the bottom of the Project tab to do what's called "New Composition from Selection".  It can also be done by right-clicking on a Comp or by selecting a Comp and choosig File > New Composition from Selection or by selecting a Comp and using the keyboard shortcut (option backslash, Mac or alt backslash, Windows).

If over time you are not able to choose options in the application, you may be experiencing a memory leak.  This is mostly likely caused by third-party plug-ins (effects), add-ons, or extensions.  The best way to troubleshoot this is to try disabling those as well as making sure that your hardware exceeds the After Effects system requirements.
There's a lot to learn about it.  Have you had a chance to go through the free Learn tutorials from Adobe?  Learn How to Use After Effects

-Warren