I can practically bring in tenants after some quick and basic fixing such as the roof, painting, carpeting and new windows.

The issues that can arise with lack of practice too can lead into trouble.

Specifically relating to 2-4 unit multi-family buildings, is it conventional practice for the owner to simply pay for water, sewer, and trash or is it conventional practice to bill these expenses back to tenants? 

I'm wondering if a mortgage service company is the way to go, or if it would be more practical to handle it ourselves.

Tenants that seem to be difficult or not paying on time, I would issue a Notice to Vacate when it best suited your personal situation to get the unit leased again as soon as practical.  

We don’t really have the option to leave as both our families live here and we’re licensed to practice law in NY and NJ only.

For the past couple of years, after noticing a really disturbing trend in the marketing practices of Turnkey companies, I've started focusing my talks on how companies can use good marketing practices and how investors can cut straight through the crap and eliminate companies that deliberately lie in their marketing.I am going to give every out of state investor looking to buy Turnkey properties or even looking to hire property management two quick lessons and five tips on good due diligence.First, ask questions. 

A practice of nickel-and-diming me to death will not have great benefit for them because it will generally not result in handing me the short end of the stick, but also reduce their share of the rental income.

Great idea...very practical. 

Landlording is a people business, I suggest you practice learning to be personable, be caring, be helpful.