1. As a landlord do I always pay for the water/sewer bill?
2. Are there other bills I should be paying?
3. Correct me if I'm wrong but isn't it normal for the tenant to pay the bills?
Find out what is attached to the property (ie if the tenant doesn't pay, you are on the hook for it). Also what is in your lease. Look at what is the norm for your area. Sewer is often paid by the owner, water depends. For two of my places, the water company won't let the tenants get the bill in their name (and if they don't pay, I have to), so I get the bill and the tenants pay me back.