is it even possible for black holes to orbit one another?

The gravitational waves detected late in 2015 were from the merger of two black holes that were orbiting each other.

If they are very close (almost touching), they will radiate gravitational waves and approach each other more closely.

But if they are a fair way apart (like the Sun and Mercury), they will remain in stable orbits for much longer than human timescales.

2. That these could be black holes (instead of stars) that are orbiting a common center of mass?

If you replaced every star in the Castor Gemini system by a black hole with the same mass and velocity, the orbits of each of them will be undisturbed. It will just be a lot darker in the vicinity.

1. We could expand this out to 8?

People have studied multiple star systems. There are some configurations that are semi-stable, if one object has far more mass than the others (like the Solar system), or the Trojan orbits inside the Solar system.

If you have two stars in a close orbit (2 stars), from a distance it will act like a single star with the sum of the masses.

If you have a pair of pairs, (4 stars) from a distance it will act like a single star with the sum of the masses.

If you have a pair of pairs of pairs (8 stars), from a distance it will act like a single star with the sum of the masses.

they would be moving tremendously fast

A black hole at the distance of Mercury from the Sun would orbit much faster than Mercury (because the mass is much greater).

You can work out the orbital period here:

https://en.wikipedia.org/wiki/Orbital_period#Two_bodies_orbiting_each_otherthey would all be unstable, erratic orbital paths

In general, any system with more than 2 orbiting objects is somewhat unstable and chaotic. They are likely to (eventually) throw one object out of the system, or have two objects collide.

The best you can hope for is something like the Solar system where the orbits seem to have settled down into a formation where they could remain stable for hundreds of millions of years (barring outside influences).

For more extreme configurations (like you are considering here), you could hope for something that continues for human timescales (thousands of years). Collisions are relatively unlikely, as a black hole is a very small target in the vastness of a solar system. But throwing one out of the system is a real possibility.

calculated what the path of these 8 black holes is at any given time, and thus is the only one that can figure out a safe way...

Travel too close to a black hole, and your spaceship (and astronaut) will be torn apart by gravitational forces.

Relativistic effects like time dilation in close orbits can change the orbit slightly.

Navigation would be more complex if the black holes have different rates of spin, as this produces a nearby effect called "frame dragging", which makes orbits diverge significantly from what Newton's laws would predict.