Haha I just started teaching a ten-year-old! I'm 15, by the way.
I have to say my biggest challenge so far is making sure my student is comfortable with the horse and knows that it will not be easy. I worry that she'll feel like she's not progressing and want to rush onto bigger and better things. Also it's difficult for me as a student to juggle homework AND training my own horse and finding time to relax!
I can't really answer the income question because I do $15 an hour, which is quite a steal in my area, being $30 for 1/2 hour the normal rate at the barns I have looked at.
I don't have an arena because of where the pasture is, but I do have a long, flat, area wide enough for 10meter circles to ride in, which I love dearly ;) I teachat my house for now, but with winter coming they may not want to continue or we may have to work something out with an indoor arena that I rent near my house, but we'll just have to see!
I use my own missile-proof trail/dressage/trot-pole gelding for her lessons, but if I were to continue giving lessons later on in my life it would just depend on the student and horse as a team whether or not I would work with the horse. If they aren't suited for each other one bit, then i'd probably not work with them. (I.E. Small, weak, inexperienced 11-year-old with a flighty, sensitive, 4-year-old Thoroughbred mare)
I love teaching so far and I look forward to it all day at school! It's a great learning experience for both of us and it's something special, knowing that a kid looks up to you for advice and wants to be just like you when they're your age. I also love being able to pass on my knowledge to the younger generation and infecting more children with the "horse bug"!