-add fan or ac for white noise and ventilation while windows are closed.more expensive measures:-if there is no wall insulation, insulate walls with fiberglass batt.

Even if the utilities were transferred, they can always go out.you should drain the pipes at the lowest level (basement) AND then shut the water down.you dont want to hold pressure in the pipes ..that's what kills them. also insulate the pipes before the shut off valve (assuming it is somewhere in the house) as they might burst as well. that's assuming there is no heat to the house. if there is heat provided ....do the same ..just in case.

For the noise a lot of older buildings have insulation that thins out over the years in the walls which makes you hear every little noise.  

Is adding insulation to your ceiling a possibility?  

Sometimes you have to insulate and protect those dreams, while they grow into reality.  

I was just over last week to look at another landlords property which my carpenter renovated in 2013 - full gut, new kitchen, new bathroom, new windows, new outside door, insulation added to the envelope.  

Short term improving the building envelope through insulation, programmable thermostats might help.As for switching to gas, price it and any rebates you get.

Which could possibly end up being more during winter due to poor insulation.

The house, built in the late '60s in Northern California, had no insulation in the exterior walls.

In a 2nd story apartment building that is as old as yours, there probably isn't good insulation, or double pane windows.