In later pregnancy, you get braxton-hicks contractions, which make the belly firm up from time to time. It is practice for real labor later on. If worried, call doctor.
First seek this answer from your midwife or doctor. But you have about 10 weeks left so you could be having braxton hicks contractions, but they don't last long.
Yes, this is very normal. As your uterus expands with a baby inside it becomes very hard. Also, when you are in labor, contractions cause a bard stomach.
