Question: I'm using a tablet with Android 2.2. Is there something like `Tab` to switch to the next form field?

Answer: 
Use a USB-OTG cable to connect a mouse. You can even make your own by cutting and soldering a microUSB cable to the female end of a USB extension cable.
Scrcpy is awesome!
It uses adb directly for backend and it doesn't block those remote screen restricted apps too. And since it's adb. You can remote control via same network wirelessly.

For linux users. It's available on most of package managers.