Hello, and welcome fellow UK-er!!!
The first question you ask is very, very difficult. Harry was the same when he was 'little' - but we didn't live with the horrible threat that you're under. What a nightmare for you
I tried stuffed Kongs, play-penning him, getting someone to pop in - everything imaginable - but nothing worked. He, too, didn't eat, drink, or play with toys while I was out...in fact he still doesn't...he just waits for one of us to come home (I find that quite sad...). But having said that - time is probably what solved the barking problem - realising that we WOULD be coming home.
I KNOW!!!! A pair of earplugs put in the envelope of the letter to your neighbour....
Your second question - well, I certainly wouldn't let Oscar off the lead, you just can't risk it. Now a LOT of people will disagree with me now...but I got Harry the longest Flexilead I could find - not the cord type, but the tape kind. To us, it has been an absolute saviour. I never use it when we're doing road-walking, but I always use it if we're in a park or somewhere that I don't know the boundaries.
I truly wish you all the very best - and please keep us posted on your yucky neighbour
Sally + Harry xx