Yes this is normal. As long as the contractions stop within a few minutes, and don't get more intense or closer together. If they continue, call your doctor!
It's completely normal. So no worries. That's actually when Braxton hicks kicks in, during or after having sex.
I don't know if it's normal but apparently it's linked to prostaglandins In semen that cause the cervix to soften. But I get really bad pains exactly like this and I'm 37 weeks.
Plus cramps in my right leg that come and go.