I use scene to see fps, it's does keep on 60. Maybe it's the move animation makes me feel laggy. Btw, my phone is iqoo neo 10 pro, dimensity 9400, Android 15.
There is no developer mode on Android (it would require more work than I can do in my spare time).
It detects a gamepad automatically, you will see a gamepad symbol on the title screen bottom-left. Something like a USB C cable might work (it works for me), or you would have to pair the gamepad wirelessly in your phone's settings - I recommend turning to the internet for advice on that one.