Can I assign my current dining room to my mayor or will this prevent the rest of my dwarves from using the room? Do I need to build him his own dining room?
Yes, he should have his own dining room, separate from the Fortress's dining hall.
When you're small you can generally get away with putting the Mayor's dining room inside the dining hall. Both rooms will be much less valuable while you're doing this, so if your gameplay style requires your dorfs to spend half their lives admiring the amazing dining room, or you care that your Mayor's office sucks, it's not a good strategy.
But if you don't care about that stuff the main meeting hall is actually the best place to put both your Mayor and your Manager. Actual nobility (ie: your Baron) should get their own office, but the doeks who do the administrative work will do their work fine from the dining hall.
Nick
When you say "meeting hall", are you referring to the Dining Room? I turn off the "meeting hall" option in my dining room to prevent dwarfs from throwing parties. Am I doing it wrong?
Also, what's the point in having a mayor? Is it just another obstacle to deal with? Guy seems more like a hindrance than anything else. I took some office responsibilities off of my leader and spread them out between the two, but that's about the only use I've gotten out of him so far.
In Dwarf Fortress there is no such thing as doing it wrong. I use a meeting hall/dining room/anything because 90% of the time I don't care about parties.
As for "why have a mayor," the answer is because the game will elect a new one every year, and firing him is a pain.
Moreover without a Mayor instead of having that dude whose masterwork mug was just stolen by the kobolds get a "conduct meeting" job, where he's consoled by the Mayor, he'll remain pissed off. You risk a tantrum.
As for other diplomats, I think some of them speak with the Mayor even after you've got a Baron, which could be a problem. besides if you think the Mayor is such a pain that you insist on de-appointing him every year, you probably tell the liaison to go jump when he offers you the even bigger pain of a Baron/Count/Duke; which means you won't have anybody who can tell the trade liaison you really need flux.
Nick