Your appendix is on your right side, very low in the pelvic region. You could have a urinary tract infection, kidney infection or a strain in that area. If it persists, see you doctor.
(PS... it would be extremely rare for the appendix to be located on the opposite side of the body).
Yes, it is possible. Any organ in your body can be on the opposite side to what normally occurs. This usually doesnt cause any problems, as long as certain organs dont end up on the same side (that is usually fatal, and results in miscarriage).
It is possible, but rarely found to be on the left side