Had unprotected sex last month while on birth control and cycle came on, this month cycle is late and I'm having cramp like symptoms, why is that?

Could be pregnancy. If you missed any pills, it's possible that you ovulated and could be pregnant, so a pregnancy test is always a good idea with a late period. Are you still on the pills or did you stop. If you stopped the pills, the next period can be delayed. If you are still sexually active and not on birth control, see your doctor about other options.
It's hard to answer. Likely not a pregnancy if on the pill. I would check a upt though. Could it be a cervical or uterine infection for the pain? Possible UTI for the pain? It's not unusual to skip a period on the pill, check a upt, if neg, my bet would be a bladder infection. Gd luc.