I don't think most antique grinders will grind well, you need ok burrs and somewhat tight tolerances. Do you have a photo of your machine?

I can tell you with certainty that grind uniformity is also very important and that's probably what you're gonna lack the most.

You can try using this tool by Unspecialty to get an idea of the grind size/uniformity without buying any fancy equipment. As far as whether your grinder is up to snuff, I think how the coffee tastes to you is the best determinant. If it tastes good to you, it's good coffee :)

Antique grinders are most likely going to be terrible as only in very recent years we have started making coffee that does not taste terrible.

How fine is fine? Fine for Turkish is basically dust. Fine for an espresso machine is smaller than table salt but not dust.

There are specialized sifters to identify how many microns large the coffee is.