Well, according to my quick search I that's the popular folk etymology, but there are other possible origins from Celtic or Brythonic like helyg (willows) or heli (salt water) and others. Etymology of placenames is often much more fuzzy than we (and tour guides) would like it to be.
No...it's likely correct. Bede talks it in his Historia Ecclesiastica. There was the thought in the early 20th C. that he was wrong (which is a fair question to ask of Bede), but most modern scholarship backs him up.
Well, I don't want to go into the rabbit hole of reading a bunch of literature about the name of a city I will never visit and likely never hear about again. So I guess I will just roll with your answer.