Hi there!
Great questions, I work for planned parenthood, and I see women with questions like your everyday.
A lot of virgins like the "pill"(or patch) because it equalizes their period, and they tend have no more cramps associated with their period. You are not unusual at all for being on the patch for this reason.
You can be honest with your doctor/nurse, they legally cannot tell your parents anything you disclose about your sexual life/history. A lot of times they may not ask why you still want it, becaiuse they know the benefits of the birth control method you use.
You are able to get pregnant within weeks of removing your patch, or stopping a bc pill. Fertility returns quickly.
Birth control basically puts your ovaries to rest, they still have all of their eggs, but they do not "push them out' while you are on bc.
There are female doctors with 2-3 children that have been on the pill for 20 years.. The pill is safe for your fertility, but some women will always have fertility problems not associated with the pill.