1990 Nissan Quest Driving without Transmission fluid.

Why was it out of fluid and did you notice it slipping? If there is a leak, it wasn't totally empty and there may be no damage at all. If you drained it and it WAS completely empty, you wouldn't have moved at all and no damage would have been done.

When the fluid is low enough, air gets sucked up by the pump instead of fluid. That fluid is under high pressure to apply the clutch packs. Air compresses and prevents the necessary pressure from building up. That prevents the clutch plates from grabbing solidly and slippage occurs. That slippage causes a lot of heat which ruins the fluid's ability to lubricate, and it chews up the clutch plates. The debris from the clutch plates can tear up the seals in the drums so the clutches will never apply properly after that. That requires a total rebuild.

It depends on whether it was slipping and for how long. If you stopped driving because it wouldn't move anymore, expect to find a lot of damage. If you stopped driving because you got where you wanted to go, it might be okay. You have nothing to lose by filling the fluid and seeing how it works, but it would make sense to have the leak fixed first.

Most of the time there's no noise.

Depends on what happens and how long it takes you to notice there's a problem. With a slow leak, it will take a while for the slippage to occur, but when it does, it usually happens suddenly, like when you go around a corner or leave a stop sign. The clutch plates can tolerate a little slippage, but it would be similar to holding your foot on the clutch pedal for a manual transmission. The longer you do that, the more heat will be generated. That clutch plate wear in your transmission builds up over many miles until the slippage occurs. Slipping due to low fluid level will cause the same amount of wear in less than a minute as normal wear causes in perhaps 100,000 miles.

What you need to do now is have the leak fixed, replace the fluid and filter, then see if there's any problems. There's a good chance, from what you've said so far, that there will be no additional problems.