I'm running the game on wine here and I've done everything on the UESP wiki for registry tweaks etc; and Morrowind runs great, save for some minor lags when looking at NPC's (when starting this problem comes when looking at Jiub). I don't know why that is cause this is a Core2 with 4 gb of memory. (OS : Debian, wine 1.3.8)

Again, this is not that much of a problem. But sometimes when I take new game, Jiub doesn't talk. He doesn't freaking ask me for my name and the gaurd just comes and stands there. I realised that sometimes I just need to click new game to fix this but then at the Census Office, Socius Ergalla doesn't start the dialogue either. It's not like its a conversation that I can initiate either.

What can I do in this case? I'm having the GOTY edition btw.

Sounds like a problem with the game's scripting system. Scripts would be responsible for everything you described that's broken in the 2nd paragraph.
There's a console command "ToggleScripts" that presumably turns scripts on and off. You could try using that to get scripts to run, but they should be running by default so I don't think that explains the issue and it probably wouldn't fix it.
Sorry I don't know what to suggest to fix this, but I think the problem can be narrowed down to broken scripting. As to why that would happen, I don't know.