SO many people expect so much of baby dogs.
The transition from being a puppy to being a pet, adult dog is slow and requires patience and a lot of training. You can't just take a clueless pup home and expect it to do everything all at once.
Keep walks short and full of interesting, fun time with you, and treats.
Carry the puppy, for now, on the stairs. You can try training, slowly. Put a treat on each step. Praise like crazy, in a calm voice. Encourage your puppy.
This isn't about laziness or stubbornness. It is about an animal who is getting used to a whole new way of living, with strangers he has no attachment to.
Take your time.