Well, let's take up those questions in order.
A couple of other people have commented on the lack of any opening under that box on the Bounty's stern, but I don't think that disproves my theory of what it is. If there were such an opening, imagine what would happen when a heavy sea came up under the stern while somebody was occupying the box. Contemporary drawings of the quarter galleries of larger ships (where we know the officers' water closets were located) rarely if ever show any drain openings - probably for the same reason. I think the chamber pot is a reasonable inference.
Admiralty drawings generally don't have dimensions written on them - just a scale at the bottom of the sheer plan, from which it's possible, using a pair of dividers, to figure out the dimensions of anything shown on the drawing. When I'm working on a model I always get hold of a copy of the plans on the same scale as the model, so I can transfer dimensions directly from the plans to the model.
I've never seen a drawing of an eighteenth-century flag locker that looked anything like that thing. The flag lockers I have seen illustrated are relatively small, low boxes (about the height of a man's waist), which sit at the base of the taffrail. (H.M.S. Victory is a good example. If I remember correctly, her flag lockers are in fact made of canvas, on wood frames.) I think you're right: there would be no rational reason for a flag locker to be the size and shape of that box on board the Bounty. But it's just the right size for a water closet.
The Admiralty drawings only show the little quarter galleries ("quarter badges" probably would be a better term) in elevation, on the sheer plan. I'm not convinced that they projected from the sides of the ship at all; they don't appear in the deck plans. Anything a modeler put on the sides of the ship that matched the outline shown on the sheer plan would be defensible.
The reprinted version of David Steel's Elements of Rigging and Seamanship (it gets sold under several different titles; any book by him with the words "rigging" or "seamanship" in the title is almost certainly the right one) contains lots of information about the rigging of merchant ships, in the form of notes added to the information on warship rigging. The slightly later Young Officer's Sheet Anchor, by Darcy Lever, was updated some years after its original publication to include some information on merchant ship rigging. The nice, reasonably priced reprint edition sold by Lee Valley (www.leevalley.com) includes those notes. Another good source is Karl Heinz Marquardt's Eighteenth-Century Rigs and Rigging. Generally speaking, the differences between warship and merchant ship rigging don't seem to have been major. I don't think a competent merchant ship crew would have had any trouble handling the Bethia/Bounty with the rigging I put on my little model.
I don't have any objection whatever to a manufacturer's putting a generic label on a ship (i.e., calling it a "typical eighteenth-century schooner" or a "typical East Indiaman.") I do, however, take exception to the re-labeling of a reasonably accurate model of a specific ship as a generic one. (An example: Revell's "Yankee Clipper," which is just the Flying Cloud in a different box.) And I really take exception to the reissuing of a kit under the guise of another vessel for which adequate documentation does exist. We know that H.M.S. Beagle did not look anything like H.M.S. Bounty. And the Cutty Sark and the Thermopylae resembled each other only from a distance - as did the Alabama and the Kearsarge, etc., etc. When companies like Revell and Heller behave like that, they are, in my personal opinion, guilty of deception and dishonest marketing.
All these opinionated rants are, of course, just about irrelevant to reality. The plastic model manufacturers have just about given up on the sailing ship. From the financial standpoint - the only one that matters to those people - that makes sense. I do wish, though, that when one of those companies decides to reissue and old sailing ship kit it would pick a good one. Rather than inflict that infernal "Beagle" monstrosity on another gullible generation, why not bring back the Flying Cloud? Or the Charles W. Morgan? Or the Golden Hind? Or the Mayflower? Or the yacht America? Or the Batavia - which, to my knowledge, never got released in the U.S.?
The best sailing ship kits represented, for a long time, the best the plastic kit industry had to offer in the way of serious scale models. It would be nice to see some of those kits again.