Qualification on these responses - my Twinmotion experience is prior to Abvent selling to Epic Games. So some things may be different now...
1. You can just export, but synchronization is the best way. With syncing, you can update your ArchiCAD model, re-sync to the same TM file, and your TM model will update per your ArchiCAD model. It is not automatic - it will not happen unless you sync again.
2. Transparency - don't have access to TM right now, but I believe if you select the material and check its settings, there is a control for transparency. With some controls you need to look for the "more" option to get to the next level of control. I haven't experienced this problem, so this is just my best suggestion as to where to start. [Edit: I don't see any transparency settings, so not sure what is going on here]
3. I don't know of any other material libraries. Abvent did a blog on how to create your own materials. That may be on the Epic site now (I think a lot of the blogs were moved over, but looking now I can't find them).
4. Yes, ArchiCAD materials determine TM materials. I believe you can work around this a bit by using ArchiCAD surface overrides. [Edit - You CAN select whether replacement affects material or just the selected object. See attch.
Hopefully some of this is helpful.
ArchiCAD 22
Win 10