Isn't it crazy how high the jumps can get?! You won't see an entire course of jumps at 7 ft though, that's mainly something they do in like, a Puissance. (if you want to see something really cool, look up Puissance on youtube!) Basically everyone jumps a jump and they keep raising it until no one can jump it anymore! The last person to jump it without knocking off the top wins.
And just a bit of extra info... the jumpers start off at level 0 (or "Puddlejumpers") which is 2'9 at rated shows. They go up in 3 in increments until level 9 which is 5'0. All "grand prix" means is that there is a bigger purse for winning (i think they start off at $10,000?). The more money you can win, the higher the jumps will be. So the $10,000 GPs are only like, Level 7 or 8? I'm not certain about that though.
It is very important to know a horse's physical AND mental limitations. A horse that physically can't jump the big stuff is going to knock down a lot of rails. That will be your biggest clue that your horse doesn't have it. :) But people have to be responsible enough to know when a horse gets nervous jumping things that are higher then what they're comfortable with and make sure they're confident at the smaller stuff before moving them up higher.
I don't think some of your questions have a set answer. When you're training a horse, you start off smaller and work your way up. You just keep going up until you hit your horse's maximum height. Some horses can last YEARS at the upper levels. Some don't jump as well after a few years. A horse should be able to last longer then a season though. Most horses won't get to the GP level and just break down. Most of them will break down along the way. Which is another reason why they're so expensive, they're sound enough to get there. (And by breakdown I don't mean just fall apart, it's more, can't stay sound when he's jumped over 5') I think there are much fewer breakdowns then racehorses (I think, but no statistics). They start racing horses at a crazy young age. I mean, most of those horses are supposed to be at their peak at like, what, 3? Most jumpers start being ridden around 3ish (and there's not as much of a hurry). Because it takes so much time to train a top level horse you're not going to see any top jumpers that are only 3. So they have a little more time to develop.
FEI stands for Federation Equestre Internationale. It's the international governing body for competitive riding. Basically makes up the rules and makes sure people follow them! You may have heard of USEF, same thing but just for the US.
Keep the questions coming! I agree, I think talking about jumping is VERY fun! :) (hence the novelesque posts...) And what better way to get your answers then to ask on here?