BA, further to the excellent advice already given, I refer you to this thread; [Got my car and motorcycle licence which strangely enough are in the Vroom, vroom forum.
Also, about getting the TW-issued international driving license, see this thread;
[Taiwan-issued International Driving Licences/Permits
I think you could just about do it in 3 weeks.
Regarding driving AFTER passing the test; you say you already have good road awareness and I assume you got this riding scooters. This is helpful and hopefully should make you more aware of two-wheelers when you’re in that big metal box!
There are certain procedures such as mirror-signal-maneuver which I don’t think are part of the test but nonetheless are very useful to get in the habit of doing as soon as possible. So yes, some lessons from a qualified, experienced driver with a foreign licence would be good.