If I have pains in my abdomen when I pee, is there something wrong with my bladder?

Probably. Could be infection, inflammation of bladder, inflammation of nearby organs (gyn). See md, get examined, get urine tested, other tests if needed.
Probably. Pain on voiding is probably related to bladder infection or obstruction, among other conditions. Need to see doc for eval of urine sample. If not straightforward you may need to see urology. Untreated bladder conditions may lead to kidney disease.
There could be. Certain bladder dieases can "refer" pain to the abdomen in general and should be further investigated appropriately.