Sounds like he's doing well. I did all the same things after my surgery. My doctor had no issue with stairs. My shower and bedroom are on the 2nd floor and I was mainly on the 1st. He told me notta prob, just be careful.
The general rule of thumb is... do what you're able without overdoing as long as you're not bending, lifting, or twisting. The sooner he's able to get back to normal activities, the sooner he'll recover. Week 4 and 5 is usually a crash week, so expect very small setbacks at that time, but they're temporary.
I let my body be my guide. If I started aching, I rested, if I was up to it, I'd do stuff.
Also note: the drugs are still in full force right now, so it's easy for him to think he can take on the world. I personally feel that the anesthesia stays in a person for quite a while and that's why some get a false feeling of superpowers
in the first week or two.
Hope that helps.