Puppy blues – needing advice on a few of the biggest issues

Kia ora from New Zealand,

My wife and I have recently adopted a 7 month old Labrador/Bulldog mix (at least, that's what we think he is). I know he's a good boy, he's good natured and responsive to training. However, I've been crippled by anxiety since we've gotten him. I find myself sobbing uncontrollably each day, paralysed with stress overnight as he's in his crate, and having trouble imagining a future where I have my life back. Like most puppies, he requires constant supervision to avoid chewing on bad things, destroying things, pissing off the cat, pissing and shitting inappropriately, and he needs constant exercise and attention. I've lost all of my hobbies and my social life and find myself forgetting to eat and shower.

Reading the stories on this sub about puppy blues has been enormously helpful in keeping perspective and optimism, so thank you to anyone who wrote something about it. I probably read it. However, there are a few things I urgently want my dog to work on in order to maintain my sanity. Any tips welcome:

Walking on a lead: we adopted our pup from a quiet suburb and we live just outside of the CBD. It is much louder than where he grew up. He's been extremely distracted on walks, alternating between sniffing everything and looking everywhere, and then being seemingly too scared to walk and just becoming a brick. I suspect it's nerves, which I understand, but how can I manage this? He's going to live here his whole life, so I want him to get used to it, but I don't want him to be too anxious.

Messing with our cat: Our pup hasn't been aggressive towards the cat, thank god. I told my wife that's the one thing that would make me give up on him. However, he incessantly sniffs the cat and follows it around and starts to chase it when it runs away. I know he's just a puppy and has energy and curiosity, but we need our cat to feel safe in our home too. The cat has been isolating himself and I'd like him to feel comfortable.

Redirecting: Usually once or twice or day, the pup gets into a mood where it feels like he's intentionally trying to make us mad. He will start chewing on things he isn't supposed to, trying to eat the cat's food, pretending like he has to pee and then not going, and other annoying things. We'd like to manage this by playing tug of war with him, or getting him to chew his actual chew toy. If we could master this, it would save me a lot of stress and 'hypervigilance', and I could relax a bit at night.

I am committed to this pup and I know the puppy blues will subside, but any advice about the above would be much appreciated. Thank you