I think rules are probably individual to each home but we had no pushing through doors before being told it was OK (that took many hours of standing at a door, with my hand on the handle, waiting for him to sit, then once he did that, opening the door a crack, if he got up to dash through I'd shut the door quickly, this was repeated ad infinitum before he got the hang of it and now sees us go to open a door, sits and waits until he's told it's OK to go through).
Reward eye contact: We spent time just working on getting eye contact, eye contact is huge with dogs they need to learn to look at us for guidance. We sat with a handful of treats, showed them to the dog then held them in a fist. At first he would dig, paw and nuzzle at our hand but the second he gave eye contact we said good and rewarded him. Eye contact was one of the first things we worked on as it is key to lots of other things. Our other two dogs were 8 weeks old when they came to us and eye contact seemed to come naturally to them but Cop was used to being his own boss and had to learn to communicate with us. Does all this sound a bit woo? I'm sure it probably does but for us cracking eye contact with him was huge. There's an article about eye contact here.
Food: we worked for weeks on manners over food, at first he had to be on a lead so he didn't lunge for the bowl and swallow it whole, we gradually built up to where he gives eye contact now before being told 'eat it'.
Toileting: we limited his access of other rooms until we'd got some where in the battle to toilet train. Clean up any accidents with a solution of biological washing powder or liquid as it helps to eliminate the odour and stops them thinking that that area is an OK place to toilet.
Leaving them: We did what pigsDOfly suggests, leave a room, wait for a few seconds then go back in and treat but I didn't reward if he was barking/whining. We then extended it to leaving the house.
We have had two dogs before Cop and we got him as a companion for our collie, in the early days I honestly thought I would only ever tolerate him as he was such hard work, in fact I was slightly scared of him but I have to say that he is the most rewarding, loving dog that I have ever owned. He has an extra special place in my heart and I am very glad he came to live with us.
Do your rescue offer follow up help? Lots do so it might be worth investigating.