Will frequent crying harm my baby who has colic?

No. No, your baby's frequent crying due to colic will not harm him/her. Colic is still one of those great mysteries that has no definitive treatment except time. Thus, many colicky babies do cry a lot (many hours in fact). Due to all the crying, it is imperative for a parent to sometimes put the baby down if they feel the crying is getting to them, and this will not harm the baby at all.
No. No it does not appear to cause any problem. But see my answer for what to do for colic. I belive there is almost always a cause which if found is correctible.
No. Babies will not "cry themselves to death" though their cries tug on our heart strings. It is not a bad idea to make sure that your child really has colic and not some other medical problem like gerd. See your pediatrician to evaluate for this and other diseases that can mimic colic.
No. It will not harm the baby. However, trying to help the colic which is a digestive issue will help the baby not cry. 1. Change to a hydrolysate formula if you are bottle feeding. 2. Try probiotics. 1/8 tsp 2x a day for newborns. 1/4 tsp a day after 2 months. 3. Try gripe water or cocyntal for colic. Also colic calm. There are many things that help colic.