“Do dental implants hurt?”

I'm not sure what your question is asking - do implants hurt? Are you asking if the procedure to have an implant hurts or if an implant just hurts normally when in function? Either way, the answer would be no, because you are anesthetized to have the procedure done, so it's not painful during the procedure. After the procedure, you would normally take NSAID-type medication like Ibuprofen, so the postoperative period would have minimal discomfort. When the implant is completed, there would not be any discomfort from just functioning on it, as there are no nerves connected to the implant.

In decades of placing dental implants, I have found that it is very rare that they hurt. Of course surgical procedures are always technique sensitive. Most of the time, any discomfort, if present, is related to a tooth removal rather than an implant.
Hope this is helpful for you.

For dental implants, you will be under local anesthesia just the same as for caps or fillings and won’t feel anything. Done right, they don’t hurt.

No ! If they are placed by an experienced dentist there should be minimal pain (less than an extraction). Once the implants are placed, you should forget it was placed and treat it like any other tooth.