It depends if the horns have thin sheaths (like deer), a bony core (like bulls), or a simply a fiber mass (like rhinos.) If they grow like a rhino's horn then they would have no nerves and wouldn't hurt if they break (no nerves).

I think that's up to the GM. A Rhino's horn continues to grow though out it's life, although the older the animal gets the slower the growth. Thing is, I remember reading something about Goblinization resulting in a massive calcification of people's bones resulting in 'bone' spurs along elbows and knees as well as horns. I assumed this was similar to a type of Scleroderma called Calcinosis (Calcium deposits that leak out of the skin at joints and can eventually harden.) The point is that if these calcium deposits continue this growth in later generations then yes, I would say they would grow back with speed depending on the age of the Troll and possibly hormone treatment. Problem is Calcinosis isn't the greatest thing to have, and Trolls would be in constant joint pain all their lives getting worse as they get older.