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

Answer: 
Give [androidscreencast](http://code.google.com/p/androidscreencast/) a try. You may already need to have USB Debugging enabled for it to work, but you've said you already have that enabled, so should be ok. It just needs a USB connection to the phone and goes over the ADB protocol.
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.