Here is one of the links to the forum page were I talk about the stuck drawings, there is one more link here when I find it I'll come back and add it also.
http://www.rubberslug.com/board/showthread.asp?T=1021&P=2
This one goes indepth a little more.
http://www.rubberslug.com/board/showthread.asp?T=919
This will work for the small remnants of paper also. try it on a small part first so you can see how well it works.
Once you wet the paper though use your finger to rub lightly and the paper will come right off maybe in small parts so take your time.
Use a cheap cel to try for the first time so you get used to the way the paper comes off the cel.
NOTE: Don't use tap water use only distilled water.
As for the cel bags, If the cel bag is sealed I don't see any problem with putting it in the same folder with your cels,Just don't use tape to seal it with as most tape is very acidic buy the bags that have the gum type sealer on them.
AS for the stuck backgrounds I would leave it alone as there is not much that can be done, But you can slow any damage by also putting it in a sealed cel bag so water from the air can not get to it.The water color paints act sort of like a barrier between the cel and the background paper,
Most backgrounds are painted on acid free papers most of the time.If you are going to store your cels with there backgrounds put the cel in a cel bag and then place it on top of your background this way you will not get the sticking in the future.
Roy