You can launch your application directly from Android Studio, either using an emulator, or your phone. You just have to be sure it's set to debug mode (which it should be by default), since that signs it with a debug key.
Or you can build it and manually send the APK and install it, which requires you to turn on "Unknown Sources" on your phone (as it would gladly tell you).
As to developing for Android in general - welcome to lots of XML + automatically generated hard coded strings + terrible APIs + Java syntax. In other words, the worst.
And that's before even starting about actually interacting with Google in any way (leaderboards, purchases, not being able to test your own product and instead forcing you to invite other people on Google+ because that's logical, and lots of other really great user friendly practices).
As to Moai - it's pretty mature and you write code in Lua. It's not very easy to start with, unlike some other popular Lua-based frameworks (e.g. Corona), but it lets you do advanced stuff when you need to, and its completely free. You'll still end up wasting your time on Google related things such as the ones highlighted above, but nothing to do about that...
And of course, it's open source and cross-platform, so that's always a bonus (you'd probably want to publish to iOS at some point?)
The drawback is that you don't have direct control over the Java-side, unless you edit the Java side. That is, if for example you want UI elements, you need to make them by yourself, and can't depend on the native ones, unless you go and make them in Java like you'd usually do (this isn't true for some things like native confirmation dialogs, which Moai does support).