Do containers respawn?

Yes it is possible to farm the containers over and over.

One of the first containers that I noticed which was locked was a level 2 container (I think it was on the back of an ambulance truck or something), and I looted it about 5 different times as I was passing it before I moved on to the next area.

With that said, since you can't tell if a container is meant to be locked or not (unless you're playing co-op with someone who doesn't have the skill), it'll be fairly hard to figure out which ones to farm, unless you luck out and get something really good the first time around.

Yes it is possible. Through experience I found that during the 'Boat Supplies' Main Quest, the Red Container that you get the 'Package' from has a Level 3 Chest. I farmed off this one, then headed back to the boat. Directly east of the boat (Where three punks are) is another Level 3 Chest, you can farm this one too. To respawn them, the only efficient way I found was to enter the sewers, then exit. After that, I just went back after them, gaining one Legendary Weapon (McCall's 9mm) in four days (a total of 30 hours of playing). I dont know if it changes from console to console, but I did it on PS3.