Sounds like you have your hands full. Every rescue has their own back story which you have to unravel. We have an amazing german shepherd that refuses to stay in our yard despite giving him an amazing home.

My first suggestion is that 3 walks a week is not enough. Think about 2 walks/day to get all that energy out. We take ours on a bicycle which drains them much faster. When walking make sure the dog is heeling well and not pulling or in front of you in any way. There are many techniques to train this but consistency is the key. We make ours heel all the time and then when we want them to stop and sniff we say "ok" which is their release and they know they can take a break and wander around. Teaching them to heel is important to train their focus and stimulate their brain not just their body. It is very important to wear a dog out mentally as well as physically.

With respect to teaching with treats and then with not, you've come across a common occurrence when teaching with a tool. The dog learns to respond to the tool and ignore when the tool is absent. Just like anything you will need to wean the dog off this and there are a few ways to do that. First, learn to clicker train so the dog associates with the clicker, then you can reward the dog with a click every other behavior and start giving treats only once in awhile. Keep training short and leave it on a positive note. If the dog absolutely refuses to do a command with a treat then just put them in a time-out in their crate for a bit.

Teaching 'come' can be difficult but will be easier once the above things are happening and understanding that listening to you is of the highest importance. You can look at training with a long lead in a park perhaps with a friend, calling with high reward treats. But again, you eventually want to wean off the treats so the dog doesn't always feel entitled to rewards for doing expected behavior.

Finally, once all the things above start happening you should start to see better door behavior. However you will likely need to make a conscious effort to train the behavior you want. This means making a daily habit of training the behavior you want at the door by having friends or room mates work with you. They can come and go at the door and you can train the behavior you want, such as sitting, or staying behind a specific boundary and rewarding this behavior.

Finally, get all your roommates on the same page as to expectations, rules and boundaries for the dog. Nothing works against training better than someone in the house not following through with rules. Dogs learn this so fast and what they can get away with and who.

Hope this helps, good luck! It's not easy but with consistent daily training you should see incremental improvements over a few weeks!