Thank you for rescuing this bunny!
As Tobyluv has said, rabbits don’t need to live outside. Most of use here have house bunnies, because the outside isn’t safe enough. Wild rabbits live very short lives, they survive as a species due to their very high reproduction rate.
Rabbits do need exercise though, and I think a whole floor for 4-5 hours/day sounds lovely. Another option would be if you could set up an x-pen, rabbits love company, as he seems to have made clear to you =) Social interaction is very important for a bunny. They like to be around their humans.
Both cats and dogs can be taught to accept a rabbit as a family member, not prey. I think dogs present more of a challenge than cats, and you can’t leave them unsupervised until you’re very sure the dog has gotten the message, and with some dogs, that would be never. (I have a GSD and a free roam bun, but a GSD is very easy to train.)
Any room a bun is free roaming in must be rabbit proofed, and electrical cords are the most important things to protect. IKEA has cable covers called Rabalder, but there are many other types available online.
These are just some brief tips, so please stick around and ask more questions as they pop up. We’d love to see pics of your bun. We have a monthly chat thread in the Lounge where we just discuss life in general, if you don’t have any specific rabbit questions.