Cal:
Just finished trailering Pearl here from Massachusetts, and now have trailered her something like 14,000 miles (yeah, that surprised me, too!), so here's what I've learned. My trailer is similar to a Kaufman open-deck car hauler: it's open in the center with full-length ramps on both sides for the wheels to sit on.
1) Should I put on the full tonneau or put up the roof with the side curtains, especially considering the car will be going backwards?
Put the top up and side windows in. If you use the tonneau it'll mar the paint as it flaps in the wind. I don't back her on, even though the exhaust would scrape when loading. Instead, I have a pair of 8' wooden planks (2X8's) which I lay on the ground in back of the trailer ramps and put the rear end of the ramps onto the top of the planks. This raises the car just high enough off the ground to let the exhaust clear when loading.
2) How about sealing the edges where it might leak in the "unlikely" event it rains during the trip? I've read several threads that suggest that the painter's masking tape works about as well as anything else and usually doesn't leave any residue when removed.
I use blue painter's tape on the top-to-windshield-frame intersection with terrific results. Leaves no residue and has held on tenaciously in unGodly downpours at 50-70mph. It also has worked well along the hood to body intersection. That's all I've done, but when Dusty was leaving Carlisle into impending storms he taped up just about every seam on the entire car. Saw more blue than white, believe me, and I doubt that he had any leaks. If I were you, I might do the holes where the side windows meet the bottom of the corner posts, then continue on down the forward door seam - that seems to be a popular point of soakage (is that a word?).
Should the hood, boot, bonnet, lid, grille (or whatever else you may want to call the various openings) also be sealed?
If you think some place may leak and cause you a problem, tape it.
3) What is the recommended way to strap the car down to the bed of the trailer? It has a wood floor.
Without actually seeing your trailer set-up, this is really hard to answer. My trailer is open and has REALLY BEEFY tie-dow rings in the bed. I have 3-foot-long securing straps with "D" rings on each end that I put over the transmission horns in the rear, and over the bottom torsion tubes in the front. I "X"-cross the front tie-down straps to keep the car centered, but leave the rears un-crossed because to cross them back there would put undue stress on the engine sump (they would be rubbing on the sump if crossed).
Once everything is connected, I cinch everything up nice and tight with the ratcheting tighteners on the cinch straps - you should not be able to get another "click" between fully down and 90 degrees up on the handle. After traveling 10 miles or so, I stop and re-tighten all straps as everything settles and stretches. I've found that, after about 50-100 miles, everything has settled/stretched it's limit and nothing much changes after that, even overnight.
Dusty, on the other hand, has "Wheel Nets". These are strap baskets that are placed over the tops of his wheels, one end is secured directly to a trailer hold-down ring and the other end is attached to a ratcheting cinch. They are then tightened to secure them. Personally, I don't care for them, as I've sometimes seen them loosen for no aparent reason, leaving the car just sitting on the trailer with nothing holding it there (that was Charles Gardiner's problem on his SAS coupe at Carlisle). I prefer the somewhat more positive strap method that I have - I've NEVER had anything loosen up on me, even after days of traveling at 70-85mph.