Is there a Android POS full node wallet apps that is open source? An app that can also stake?
I think the short answer is no, there isn't an Android full node app. Being a full node would requiring downloading and storing the entire block chain, and that is too much data for mobile devices.

I don't know of any mobile wallets that stake. And you are right that many of the apps are just the QT code transformed to Java. I think it was done this way on purpose so as to ensure that the two references are bug-for-bug compatible.