Really depends on the gun to some degree. There’s collectibles that are worth more left alone, especially old stuff pre modern ammunition. But lots of old but not that old stuff its more or less expected you’ll fire it to test it works on receipt.

Only if they are claiming it still works and are asking for more money due to that. And still, only if you care enough to verify it works as they claim.

It depends, but the general rule is that the older it is, the less people want to see it in active use. At some point it's about preservation over anything, but there's also the safety concern! A firearm is a very dangerous thing in failure mode, so at some point a firearm is both too historically valuable, and too damned dangerous to fire.

Source: Forgotten Weapons and Royal Armory youtube channels

Why not? There are people out there that manufacture their own ammunition. This wouldn’t surprise me at all.

That would depend.

As a buyer, you would need to decide for yourself whether you want a guaranteed working firearm or not.

And in many cases, the owner will test fire the firearm before putting it on auction anyway.

Old Martini Henri rifles, dueling pistols, even muskets in some cases.

Why not?