I had a normal period 4 - 5 days after I had intercourse. About 14 days after the first day of my period, I had spotting once with nausea that I've had since then with lower abdominal pain. Could this be associated with ovulation or pregnancy?

Yes it can be associated with either, or neither. No way to tell anything from this.
You will need to wait and see if you miss the next period to really start thinking pregnancy

Now, it seems that I'm starting another period with menstrual bleeding, cramping, nausea, and back pain. Is this normal?