First of all congratulations on thinking about adopting an unwanted bully
Because his rough start he will need a time and patience with his training -it is not impossible but with dedication and behaviour training you are not only saving a bully you give him a happy life
Lets start with jumping this is how we deal with it time and time again
You need to teach an advanced sit. It is the command that gives you most control. Get him to sit every day of his life in as many situations as possible. Putting down his food, putting his lead on, while you open the door, at the kerb, while greeting people. If it's an excitable siuation, like greeting people, have a titbit on his nose and let him nuzzle it to keep him there. If he's sitting he can't be jumping up.It's the most neglected training of all. Because 99% of puppies will sit, most people don't bother with training the sit further. You need to train him to sit, in a normal tone of voice, 100% of the time in every situation and to stay there until he is released. It won't happen overnight and will take lots of patience.
For example: Opening the door.
Put him on the lead and tell him to sit. Start to open the door. Immediately he gets up, shut the door and wait for him to sit again (you probably won't need to give the command again). Repeat and repeat until you can open the door without him moving. The only thing you have to say is 'Sit'. You can quietly say' That's a good sit'. Keep relaxed all the time. Say nothing if he moves. Not only are you getting control over him, he is learning self-control. Same rule applies when visitors come around xx
Potty training you have to start from scratch as you would with a puppy ,basically you take dog out often preferably leashed to the designated area in your backyard once he do his business reward with a treat and a lot of praise ,he will eventually understand that going porgy outside means treats and fun stuff and he will start asking to go out -this will take some time -how long? All depends on a individual dog but it is not impossible ,gradually you will replace treats with just praise -we still give a treat now and again to our girls to remind them were to potty and that they done a good job remembering it ;-)
Please keep us posted