Could I have my period one month, and not the next and still not be pregnant? It goes sex (on period)=>period next month->late this month.

Do a quick HPT. You can actually get pregnant during any time of your cycle, but the chance is highest during/around time of ovulation (which, unfortunately, is very difficult to tell exactly when). Since home pregnancy tests are quite easy to do, fast, and highly accurate, i suggest doing a hpt. If you are planning for pregnancy, eat well, exercise, regularly, and get adequate sleep. Consult doc. Good luck.
Yes. Women can have irregular cycles. Missing your period does not definitely mean you are pregnant. Please see your docotr.