with a great company in Tainan
with a ... a ... you what now?
Is there any general knowledge that I should know about life in Tainan?
Life's what you make it. Tainan is a pretty nice place to live - personally I like it better than Taipei. It does get very hot this time of year, though, so be prepared for a bit of adjustment time. There are lots of "expat" type bars, if you like that sort of thing, the HSR station is not too far away, taxis are fairly easily available so you don't need to drive ... any particular concerns?
How easy will it be to find an apartment?
I strongly recommend you ask your school to help with this. You should be able to get a nice apartment for ~$10K. There doesn't seem to be any housing shortage in Taiwan, generally.
How hard is it to buy a scooter?
Any idiot can do it. Any idiot usually does, so stay off the roads for a couple months at least and take time to observe. Take your (scooter) driving test, if only to drive home the point that nobody on the roads is qualified to be there. When you can make a clearly-informed decision about trusting your life to a swarm of mouth-breathers who think a motor vehicle is a toy, then
buy a scooter. You need to bring your ID and (usually) your driving license. Unfortunately Tainan doesn't really have any public transport, and although taxis are cheap, it does tend to add up. And Tainan is a big, sprawling city so I guess you'll get one eventually. Just be careful, is all.