There is a current shortage of commercial ammunition production capacity because of demand. When demand exceeds supply, higher prices can be expected. Capacity can not be increased quickly or cheaply in an industry that has been faced with too many feasts and famines.
Yes, and the raw material shortages are very likely connected to the war. It seems like that an obvious and significant pressure on the whole industry.
No, they are almost entirely related to demand by China. It started with steel about three years ago and has now reached almost all metals except aluminum. Apparently there is not much aluminum used in China, yet.
raw material price increases are basicly a product of increased Chinese economic output (and perhaps the olympics) hogging copper (and perhaps lead, for their lead paint) production.
Yes and no, the use of copper and tin for ammunition brass and bullet jackets is probably is not the major use of those materials. The same goes for lead, which is used in batteries and electronics (as are copper and tin). Powder is pretty much unique, although the major use of it's constituents is fertilizer, but I also suspect there is plenty of it around, plus plenty of capacity to make more.
You have to remember that even though we now have a shooting war going on, the military is much diminished over what it was even as recently as 1990.
However the shooting war is likely affecting surplus ammo prices, basically there isn't much surplus around, except from uninvolved countries. The military is shooting it up in training, rather than putting it out on the surplus market. That in turn increases the demand for new production ammo, as well as decreasing the downward pressure on prices from the surplus market.