Yay! Welcome to the club without getting hurt! Jumping tends to be the times that you fall off the most, haha. Try bareback jumping sometime, you just might fall a whole lot more!
I fell off on my horse before jumping. I lost my left stirrup while riding over a jump. Or rather just before it. Jumped it rather well, stayed on...but that darn horse didn't go stright to the rail like he was suppose to. He dodged left and....well....PLOP. Bruised a joint in my finger, but that was the worst of it.
As to your question about leads...try it on the flat, not jumping to learn how to feel them. It took me a really, really long time to "get it right" by just feeling it. What you can do is feel your hips: If you are on the correct lead, your hips move/swing with the horse and it is comfortable. But if you are on the wrong lead, your hips will swing out to the outside. It feels choppy-ier. Not bad where you think "omg what is this horse doing!" Just try practicing it. When you can feel it I'll give you one more tip I've found works -most- of the time, tho not all: for jumping, as you are going over the jump itself, and landing, put more weight in the stirrup that you want the lead on. For example, if you want your horse to land on the left lead, as you are going over the jump, put more weight/shift your weight to the left stirrup. That will help him find the right lead as he canters away. It's worked pretty well for me, esp on a horse that isn't so good with her leads!
And most of all, have FUN!
Jumping is as close as we can get to flying.