1. I don't understand what you mean. Room size does matter for room value, you can easily fulfil a noble's rooming requirements simply by assigning them a huge room, bare except for the required piece of furniture. And with 'huge', i mean something like 10x10 or more.
3. as others said, high-quality furniture does a lot for room value, but it's the raw monetary value that seems to count: a low-quality piece of gold furniture is worth more money than a masterwork piece of stone furniture and should give a bigger bonus to room value. Furniture encrusted with valuable gems massively increases in value, especially when the decorations themselves are of good craftsdwarfship.
Finally, the 'base material' of the room itself also matters: 'flux' stones - marble, limestone, dolomite - have double the normal value, obsidian is rated triple, ores other than bismuthinite at double or more (much more in the case of silver and gold), gem stones count at least double, the more common 'valuable' gems have 20x value. These materials can boost the value of rooms considerably not only when they make up the walls, but also if you mined them away and construct rooms on the floors they left behind. A room with a native gold floor is quite valuable, and this value shoots up quite a lot when that floor gets smoothed and engraved.
Regarding the 'good bedroom' comment above - a dwarf will consider a bedroom 'good' if it's better than what they require, and a common dwarf requires no bedroom at all (although they'll get a tiny bit unhappy if they lack one). A 1x1 wall-less room containing a XXglumprong bedXX on a vomit-covered muddy silt floor is a 'good bedroom' for Urist McPeasant.
Re: mayors - instead of re-assigning the room, you can also re-assign ('replace') the mayor. Other than elections, changes of mayor through nomination will not end standing mandates, which can become difficult to keep track of if the ousted mayor isn't a noble/administrator.