Up to how old can you safely shoot ammo? If its old and stained, can it still be safe to shoot? Does the brass casing become "metal fatigued" making it prone to case ruptures or separation?

I've shot some ancient ammo.  My only problem is sometimes it has no power or just pops, this could lodge a bullet in you barrel.  As far as the casing blowing apart I think that would be a case of new ammo stored in a corrosive environment.  If the ammo is old and it's casing is degrading then it probably won't be at the same power as modern equivalents.

I have fired ammo from 1925 303 british, and 50 year old .38 with fuzzy lead no probs.

If it's stored correctly, ammo should last a lifetime.

I've shot 1915 8mm, some 1909 .303 and had no problems whatsoever.

"storage" is the key word here. The older it is the more chance the storage conditions will be unknown. Pull a few bullets and look inside. If there is a reddish rust colored powder present or if it has a very strong ether like smell, don't use it. Look for corrosion inside the case. Be advised all pre WW2 ammo is corrosive and if you use it make sure to clean properly afterwards and then again in a few days as this stuff eats bolt faces and bores.

Old guy at my club showed up with an old colt cap and ball pistol that had been converted (at factory?) to shoot .38 rimfire. Back in the 1930's this guys father had taken this gun for some money owed him and gave it to his son as a toy when he discovered he could not buy ammo for it.When the kid was 15 or 16 he took his paper route money and took a train down to New York to Bannermans. This was a surplus arms dealer from the civil war up thru WWII? He buys a case of .38 rimfire copper case ammo made in the 1890's.
This would have been 10 years or so back,about 1/3 would fire normally,1/3 would go off on the second wack after turning the cartridge,and about a 1/3 wouldn't go at all . This ammo was a mess,copper case all green and fuzzy,lead bullet all white and frosty. It was a real kick shooting ammo that was very close to being 100 years old. This old gent would shop this ammo around at gunshows,selling each 20 round box for 30 or 40 bucks which is about what he paid for the 1000 round crate. The stuff we were shooting up was
the odd boxes that had got wet or had been chewed on be mice.
This stuff was a very weak load from day one, 80ish gain bullet going 600fps.

Take the number 8 aand rotate 90°.  You will be past your experation date before the ammo is under ideal conditions.

when the dont go bang when the hammer strikes

It's like wine. Stored well, it'll last a while.