You should have minimum 5 ft but 6 ft is ideal. I've played pool where tables are 4 ft from the wall and it is too close. The standard pool cue length is 57" and the draw length is about 6" so 5 to 6 ft would be ideal.

You can have as it as large as you want basically.

If you are going to the effort of retiling the fireplace surround, would you consider going to a bit more effort and creating a full wall unit which incorporates the fireplace and the TV, with extra shelves and cupboards to display and store? (I also have reservations about the heat and the TV and associated wiring.) This may also address the lack of symmetry associated with the location of the fireplace, if that is a consideration. Do you use the fireplace often enough to justify keeping it? Alternatively, a wall unit on the left hand wall, which is where the power and TV points seem to be, may be the best solution - as previously suggested. All the best.

There is nothing worse than ceiling-mounted lights--harsh shadows, flat lighting. They are strictly for utility. I would put a large-ish, shallow cylindrical shade on them and put nothing more than a 15-watt bulb in them. Use them strictly for lighting your way as you walk through the room. I agree with Vincent; the chair in the corner doesn't fit at all, nor does the one under the A/C unit (put that one with its mate behind the love seat). And the curtains look smooshed. I think the problem with the bookcases is that they are uninteresting. Did you buy books-by-the-yard? What are all those identical books? They are visually uninteresting. I'd get rid of some of them and get some colorful ceramics/glass/photos. The room is absolutely overwhelmed with furniture. It needs one less love seat. Do you really need all of them? Pushing them against the walls/curtains so tightly just visually emphasizes the fact that there is too much furniture. I don't think a mirror above the fireplace will work. When people are sitting down (which is most of the time), all they will see is a reflection of the ceiling--the plain, white ceiling. Get some real art in there with some color.