2. If I assume that nothing else is on that circuit except what I connect to it, what determines the 7.5A rating? Is it a combination of the gauge of the conductors supplying that plug and the overall bike load capacity?
3. What could be the potential consequences of replacing that 7.5A fuse with a 10A fuse?
OK, I'm an electrical engineer . . . and my reply is worth just about what you're paying for it . . .
The 7.5A rating is determined by the smallest gauge wire used on that circuit, with a bit of conservatism. If you pull 7.5A from that circuit all day long, nothing bad will happen, assuming that everything in the circuit (like connectors) is in good condition. I don't recall the bike's maximum alternator output, but it's not huge, and that isn't directly related to this circuit's fuse choice.
Installing a 10A fuse in this circuit isn't a great idea. Yes, you will get away with it so long as you're not continuously pulling 10A, but I would guess that if you draw 10A for, say, half an hour and touch some of the bike's wiring that's on that circuit, it will be warm to the touch. Will you burn up the bike? Probably not, but you're pushing it. If everything is in perfect condition, you likely will get away with it for a while.
My strong recommendation is to run a properly-sized wire, fused at 10A, directly to the battery. That's what I do, and it doubles as my Battery Tender hookup (I made up a pigtail that plugs directly to my Gerbing's jacket liner and pants controller).