Yes it can be very painful. It also causes your uterus to have contractions. After a couple days the contractions stop and your nipples get used to it.
It can be uncomfortable the first couple weeks while you adjust, but so long as baby's latch is good it shouldn't be ungodly painful. After the first month it became routine for us and definitely didn't hurt at all. Lots of coconut oil ;) ice and heat felt good too during the adjustment period.
No. If it hurts you're doing It wrong. I've breastfed all four of my kids. I'm still breastfeeding my 1 year old. It's the best :)