1. I think this will depend on state and local laws. In my state, if there are any utilities on shared meters, we as the landlord have to pay it, so it's included in the rent. I agree with Johnny about doing what you can to minimize it. Luckily, by being next door, you'll notice things like tenants leaving windows open in the middle of winter.
That said, if you can get separate meters, do. In my experience tenants don't compare apples to apples when looking at the rentals, and won't consider how much they'll save by not paying for utilities.
2. We have a rental on our property--an apartment above a detached garage. The way my CPA does it is this: he takes the square footage of our house plus the rental, then deducts a percentage of any shared expenses at that ratio. So for example, the rental is about 1/3 the total square footage, so shared expenses like property taxes, landscaping, driveway maintenance, garbage, etc. are considered rental.
Any expenses that are directly just for the rental--plumbing repairs, painting, cleaning, etc.--get counted as pure rental expenses.