Ok here's my advice, not all you will love!
Keep the harness on and let him get used to it. Attach the leash for 10 minutes throughout the day even when not going outside. Again just getting him used to the evil leash.
For the stairs, This is the part you're not going to like, I recommend that you don't allow him to use stairs until he gets to the point where you can no longer carry him. When they are young their little bones are very soft and can cause permanent damage to their joints going downstairs. If it's possible, it is best to not let them use stairs for as long as you possibly can, even forever. If they're short quick stairs it should be okay, but if they are steep it is not advised.
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