I would keep him tied to you at all times. When you can't be right with him - crate him. It's not ok to potty in the house, and he needs to learn that. Keep him confined to one part of the house- and gradually allow him more freedom. Treat him like an 8 weeks old puppy. Belly bands are a really good tip too - I've seen them do wonders to makers.
When you are walking, try giving a 'leave it' command, and keep walking. I don't allow Casey to mark when we are walking, it doens't make for an enjoyable time. He pees near the beginning, and that's it. No dog NEEDS to mark. Casey gets along just fine without it.
How big is Zack? Puppies eat more food than adult dogs do. My little lab mix pup eats about 1 cup of Orijen a day - split into two meals. She poops twice, after each meal. Works very well - she's pretty much housetrained.