Those are all perfectly legitimate questions. I agree with George W.'s answers. I have reservations about the old Alexander Magoun book (his reconstruction of the Mayflower's hull is pretty awful, and Constitution enthusiasts hold his discussion of her history in very low esteem), but I think its points about seventeenth-century rigging are generally sound. We need to bear in mind, of course, that there's virtually no firm information about early-seventeenth-century merchant vessels.
The lower yards most emphatically did slide up and down the masts in those days. The topsail yards were quite small (generally about half as long as the lower yards) and, in heavy weather, frequently got sent down, presumably to lower the ship's center of gravity. There are contemporary pictures of ships in storms with their topsail yards sent down and their lower yards tilted radically, so the exposed sail area is almost triangular. The lower yards also were used as derricks for handling cargo and other heavy weights. And it appears that lowering the lower yard was often - though not necessarily always - part of the routine of furling the sail.
I have in front of me at the moment a fine, recent book called The Tudor Navy, 1485-1603: The Ships, Men, and Organization, by Arthur Nelson. On p. 107 of it is a beautiful, full-page, black-and-white photo of the Mayflower II, with her sails furled, her topsail yards lowered to the caps, and her fore, main, and mizzen yards lowered almost to the deck.
The use of the belaying pin, and the date of its initial appearance, is a most interesting subject. It looks to me as though the "pin rail" on the inside of the bulwark is a relatively new concept, probably dating from sometime in the eighteenth century. (I put pinrails like that on my model of the frigate Hancock, which was built in 1775-1776. In retrospect that may have been a mistake, but I don't think anybody knows for sure.) I believe some belaying pins have been found in the wreck of the Mary Rose, which sank in 1545. The belaying pin certainly was an obvious concept; I wouldn't be surprised if it turned out to be older than that.
Bluejacket (www.bluejacketinc.com) makes some nice Britannia metal blocks and deadeyes (including the old heart-shaped ones) that would be highly appropriate for this model.
In earlier posts I've mentioned the Mayflower II, the replica that crossed the Atlantic in 1957. I have a great deal of respect for that ship; she's one of the best full-sized reconstructions of historic vessels ever. A lot of research has been done since William Baker designed her (and she's now considerably older than the real Mayflower probably ever got). But to my knowledge no later researcher has ever identified any major mistakes in either her design or her rigging. Photos and drawings of her are good sources for modelers.
Incidentally, I'm currently reading a new, best-selling book on the subject, Mayflower, by Nathanial Philbrick. It says scarcely anything about the ship (the Pilgrims' crossing of the Atlantic is over by the end of the second chapter), but it's a fascinating, somewhat revisionist view of the whole subject. The typical American's understanding of the Puritans and the Pilgrims is heavily influenced by mythology. There is, for instance, no historical reason to associate the boulder now known as "Plymouth Rock" with the Pilgrims; the story of how that rock got its current hallowed status is both interesting and amusing.
The Mayflower is an oft-modeled subject, but certainly a worthwhile one. One big advantage of a modeling subject like that is that it allows plenty of room for individual interpretation. You aren't bound by what Magoun, Anderson, Baker, or anybody else says; any of those individuals would cheerfully ackowledge that his reconstruction of the ship involved a great deal of guesswork. Good luck.