1. I had a 1 qt widemouth Nalgene bottle full of water sitting in my kitchen for about 2 years, and I recently opened, sniffed, and tasted it, and it seemed just fine. I didn't actually drink it though, no point asking for trouble.
2. The preferred water packaging for emergency kits these days seems to be those 4 ounce foil pouches or 8 ounce aqua blox. They are sterile and sealed and have 5 year expiration dates. General advice I've seen about normal containers is rotate out the water every 6 months. Also, I've heard you should put in a drop of clorox per gallon of water (?) when you store it (I didn't do that with the quart I mentioned).
3. I guess if you drink from the bottle and then let it sit for a few weeks, stuff can grow in it, but why would you do that? Normally once you open the bottle you'll finish it within a few hours, or maybe a day. That shouldn't be any problem. It's normal to do that when hiking.
4. Packing a lightweight plastic cup is no big deal. It doesn't weigh much, and you can fit other stuff inside it, so it doesn't use much bag space either. The cup is useful since you may have something other than water to drink (e.g. tea, soup, whatever).