I don't know if it's "normal", but it also hurt for me the few times I've had sex. Even when I've tried putting something in there as a dildo to see if I'll feel any pleasure from that, it hurts a little (not as much as intercourse but still). Even when I'm super wet and the object isn't that big it happens.
For me, yes. I have a tilted cervix which might be why. Apparently you can tell if you have that by whether you normally get a pause in your period or not.