Would be very uncommon for a 14-year-old girl to have bladder cancer?

Very rare... Usually these cancers are low grade and have good prognosis. The two most common in this age group are transitional cell carcinoma of the bladder (tccb) and papillary urothelial neoplasm of low malignant potential (punlmp). Given that these are so rare, it is important to have both a pediatric oncologist and urologist involved with treatment decisions and follow-up plan.
Yes. This would be very unusual but not impossible, and would raise the suspicion of an unusual type of cancer at that age.
Yes. It is uncommon, but it happens. It is unknown exactly why, but there is an increase association of bladder cancer in young patients with augmentation (bladder and intestine are surgically combined to increase bladder storage). Bladder cancer is still a very uncommon disease in a young person. Bladder cancer risks: smoking, industrial dyes, parasitic infections..