>>11621411. Plastic. Their primary design advantage is that their circumference is big enough that bears can't get a good grip on it. OPs bear can with the twist on top is falling out of favor because some bears figured out that if they stomp on it just right the lid pops off. Better bear cans have recessed lids with locking tabs.
2. No, but most ranger stations and some camping stores like REI rent bear cans.
3. You don't have to hang bear cans but some people do. Generally it's recommended that you at least wedge the can amongst some rocks or logs to make it harder for bears to get ahold of.
The only places that require bear cans are the very busy parks like Glacier and Yosemite where bears have become acclimated to humans. Most state parks and National Forest areas don't require them and you're fine just hanging your food sack from a tree.