AFAIK, there is no canonical time in relativity. There is the "local time", which is what your wristwatch shows, and the "time in place X", where X can be Earth, Mars, or some spaceship. These times might not be in sync, and they might even be distorted. Because, if place X is moving relative to you at a significant percentage of lightspeed, their seconds will be longer. Also, the further X is, the blurrier the concept of simultaneity becomes. Which makes the question "what time is it _now_ in place X" moot :)

We'll probably come up with something similar to time zones once we become an interplanetary species.

"Local seconds since 1970", vs. "Static seconds since 1970".

You don't have to go to science fiction for this. Science fact will do. On Earth, with Atomic Time, we already have to account for general relativistic effects. Doco from the BIPM (the SI Brochure) already talks about accounting for them across the sizes of the measuring devices.

You'd just use some math to remove the influence of the black hole. Or for a more hands-on answer, you could have some reference beacons that are significantly further away from the black hole.

In a broad sense, the answer goes like this: Almost everything in the galaxy shares an approximate reference frame when it comes to velocity and special relativity. For general relativity and gravity, that's obviously a distortion so it doesn't count.

In the long term, to prevent very minor drift, we can use quasars as a reference.