Checking heart rate 100 times a day, by placing finger over neck, can it damage the artery or nerve at that location in neck?

Maybe not, but...: In the course of normal human events, throughout all of history, there has never been a need to check one's neck pulse 100 times a day. That means nobody knows what could happen if a person were to do that (and nobody is going to do a research study on it). A person who does things that are normal for the human body, has a much better chance of avoiding abnormal or undesirable outcomes.

Heart rate: Not a smart idea. There are inexpensive new wrist instruments that will check your pulse and blood pressure. Check the results on alternate mornings and nights. PS: Don't go to the Pharmacy for this device - it's too expensive. You should be able to purchase the device in one of many other stores and the cost is about 75% or less of what you would pay at the Pharmacy.