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.

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

What about a 17th century dueling pistol?

I think in this case anyone would be wise to fire a modern reproduction rather than the original article. After all anyone with the money to collect that sort of artifact can certainly afford a replica to play with.

...And modern replicas tend to be safer when you pull the trigger.

Well, if you count making a new stock and barrel to mount the original 17th century clockwork gubbins to, may I present:

https://forums.somethingawful.com/showthread.php?threadid=40...

the GP's example of WWI is actually sufficiently modern that you could very well just be firing normal center fire .45 which is readily available https://en.wikipedia.org/wiki/.45_ACP

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.

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?