No. All you need is to create the prefix, and enable it for that forum (edit forum, Tags & Prefixes tab).
I don't know why that would be. Try rebuilding the tag cache, under tools.
My system leverages the built-in tag system, yes. But there's more to it than that. The Tags page you were looking at shows all uses of tags and prefixes across the entire nsuite, and lets you edit or delete those in bulk. You don't create tags on that page. You can also allow open tags (users can set their own), in which case those tags will not be under the Posting > Tags settings, but their usage will be shown on my Tags page. Hope that makes sense.
Okay, well, I need a log of it so I have something to go by. Try this: Make the error happen, then go to that uploads/logs folder and find the most recently modified file(s). Please send those to me.
I haven't seen such an issue. Nothing should prevent you from applying tags to a topic. If you can send me forum details to investigate, though, I'll see what I can figure out.
Prefixes would seem most appropriate--that would make it show up before/in the title everywhere, whereas tags don't always display. I would create those four prefixes, use the bulk add tool (not working for you, I know; I need more info) or a saved action to apply those prefixes to all topics in their respective forums, then move them all into your new unified forum. Then set up the new forum so that all four prefixes are active, and users are required to select one.
Yes. Each forum has its own setting for allowed tags and prefixes. Sounds like you found that though,