Well, since the heavy hitters don't seem to be 
hopping in with good advice, I'll just say what 
my practice is.

1.  I've heard various methods for freeing cels 
that are stuck together, and even tried one on a 
$10 cel.  I don't know that any of them work 
safely without having the paint flake off the top 
layer onto the bottom, leaving you with two 
damaged cels.  I'd leave them stuck together, but 
you could try inserting a piece of clean felt or 
cotton cloth between the layers as far as you can 
go to get some of the dust and dirt out.  Don't 
stress the stuck-together-parts.  

2.  Judging from other cels I've bought with 
backgrounds, the common practice is to ca--
arefully use a razor blade to cut the tape at 
the point that it contacts the cel, so that you 
free the cel from the background.  Ultimately the 
cel is gonna want to stick to the background, and 
then the paint on the background will want to 
flake up onto the back of the cel.  So you're 
better off bagging the two separately.

If you can get the tape off the background 
without damage, you're better off doing so.  The 
tape used in studios, in my experience, is very 
much non-archival and will dry out and yellow, 
discoloring everything it touches.  If you 
can't ... well, you can't. But it will dry up and 
fall off sooner or later anyhow.

I'm reminded of the man with the creeping 
Oriental crud (a mythical incurable VD) who went 
to several Western doctors, who all had the same 
advice: cut it off.  In the end he went for one 
last opinion to an Eastern alternative medicine 
practitioner who said, "Oh, no, no, don't cut it 
off ... two, three weeks, it will fall off by 
self."  

As for cleaning cels, I've just used a damp rag 
for dust/dirt and, at times, cornstarch to help 
clean off tape residue.  Others might have better 
advice.