Is it possible to prevent or otherwise hinder the decompilation of your own applications? Programmatically or otherwise?
You can at most make it difficult to analyze your app by using obfuscators like proguard. You can put logic into NDK compiled c++ libraries. Hackers will still be able to decompile, modify, distribute, ... your app. I know this from experience, its better to put your time into new features than spending too much time on protecting your app.
... of course you can move you app logic (whatever you want to protect) online.