IF properly stored (cool, dry) I am not sure that modern smokeless ammo HAS a shelf life. I am shooting 8mm Mauser from the 1950s, and .303 Enfield from the 60s now. I have a few thousand rounds of 7.62 Russian from the 70s, and it shoots fine. Moisture and extreme heat seem to be the enemy. Late 1800s ammo used mercuric primers, and those seem to die as Mercury reacts with the brass casing, but later pimers do not seem to have the same problem.
Stored in moderate temperatures and low humidity, ammunition can be stored for decades.
It can fire .32 Smith & Wesson and .32 Smith & Wesson long ammunition. These are the only ammunition types it is designed for, and is NOT compatible with other types of .32 calibre/7.65mm ammunition.
You will have to have it checked out by a good gunsmith. There is more than one type of 7.65 ammunition.
It depends on the type of ammunition.
18 or 21 depending on if you are buying long gun or hand gun ammunition
Wiener
Bullets are not likely to do you any good. You can not reload rimfire ammunition. You need to search for loaded ammunition.
If the barrel has 5.56 printed on it or you have verified with the manufacturer that ALL of their barrels are good for 5.56 ammunition.
A cool, dry place
No, over time this can damage the spring mechanism that pushes fresh ammunition into the chamber.
DO NOT ATTEMPT TO FIRE MODERN AMMUNITION until a good gunsmith checks it out.
More than likely your barrel will say .22 Long Rifle only. So, you can use any .22 Long Rifle ammunition.