Number one, congrats! How exciting!
Glad you asked a ton of questions, a good breeder will be more than happy to address all your questions and concerns.
Picking him up and walking him downstairs should be fine, can't see why it wouldn't be.
You really shouldn't be taking him out in public much until he has had all his shots, I believe the last set of shots is due around 4 months. After that doggy daycare, obedience/training classes, puppy play dates, are all great places for your bully to meet new people and pups.
From my own experiences I think its important to neuter young, I would never again wait until 6 months.
If you have any more questions always feel free to post them and again, CONGRATS!!!