I must admit, I've never really looked at that new design of space station before! It is an interesting shape, sort of a precurser to the ST3 mushroom maybe? Anyway,
judging by the other starship docked and assuming it is scaled to the "official" length of 947' (230' high) then the space station would be 1,330' tall (not including the spire and dish) and around 1,250' diameter. These are only very rough "eyeballed" figures, of course.
Regarding your other points:
This is a good example of the Season 2/3 cabin side-corridor screwing up any possibility of a walk-in closet or ensuite bathroom. When Kirk enters his cabin the side-corridor is clearly visible, plus a crewman actually strolls off down it:

(click to enlarge. Also note the odd angle of the corridor wall and the blue patch where the Agony Booth controls were in a previous scene!)
Later, the Captain's Woman exits the cabin through the cabin's side door to change her attire:

(click to enlarge)
The curved wall with recessed shelving (recycled from Pike's cabin in
The Cage) is clearly visible, along with a small table and chair - and we know from the previous shot that the side-corridor would pass straight through the whole area!
Fortunately the episode never specifies what this area actually is. So, while it may seem to be another bedroom, bathroom or oversized closet (it's a lot deeper than Rand's closet) the geometry of the earlier shot dictates that this must in fact be a stretch of corridor with a rest station opposite Captain Kirk's third door. While a seemingly odd solution, there is at least space to include all the visible elements from both shots.
Sorry to go on, but that side-corridor was an unnessary addition to the set IMHO and causes a lot more problems than benefits.
I agree, there are several shots (and one reverse shot) that clearly shows the presence of the other room in Garrovick's quarters, as well as the circular wardrobe cabinet. While there
could be a bed present for Garrovick's roommate however, it would mean that all the drawers and storage were in his roomie's half, an awkward arrangment at best. If some of the crew are sleeping in single beds instead of bunks, why not give them a single room? (
see my earlier sketch)
I could certainly buy the idea that he was a security specialist (or someone with double training) however.