have fired up the hot water heater in the apt. that was turned off for
3-4 months but neglected to drain it. i'm getting rust in the water -
is the boiler on the way out or is this a result of the water sitting
in the tank?

If you have galvanised pipes it is normal, either way dont worry

I just ran water from a sink faucet that hadn't been used in months,
the water ran rusty for a about 2 gallons or so. I have ~50 year old
galv steel pipes.

either drain the tank now or just use up the rusty water as needed.

if the rust goes away you're probably fine.

cheers
Bob