The size of the android application made in EE is very big about 20MB (even if it is a simple application). Maybe I am doing something wrong. The question is: is it possible to convert it to smaller size. When I built it I used compress but it's still has got about 20MB...

The only thing you could do is replace the "engine.pak" with compressed one, everything else is compressed already (if you select data compression).
engine.pak isn't currently compressed