Sorry, I have no idea about 1, if its an Android don't you just press, look for a local provider, or does it switch automatically?
As regards 2, I've been told that in that area of the UK Vodaphone is best? No idea if that's accurate or not?
I was hiking in that area recently and I use a Giffgaff SIM card (piggybacks off of O2 I think) I never had any problems, a good signal everywhere. I just pay £10 PAYG, more than enough for two weeks for me. When I'm in a pub or restaurant I use their WIFI.
When on Hadrians Wall are you going to find the tree that was the star of the Kevin Costner film 'Robin Hood, Prince of Thieves' Still famous today!
Does your phone accept any SIM card or is it locked into one brand only?
I'm sure someone on the Forum will give you the correct answer soon.