It is not a myth, and it will hurt your cels, 
although (like real global warming) it won't 
strike like The Day After Tomorrow and 
simultaneously tear the limbs off your action 
figurines while leaving blackened corrosion spots 
on your wall scrolls.  Still, to answer your 
questions ...

YES!!!
Yes!
Maybe ... though cels I've kept in the dark for 4 
years now show no visible change.
No, sadly, though UV resistant glass will slow 
the process a little.
Yes.  

How quickly?  Well ... I framed two cels for my 
daughter in Dec. 2000, and they have been hanging 
on internal walls (no direct sunlight) for 3 and 
a half years now.  Both are still presentable, 
but both show visible weakening of lines, most 
noticable when the trace lines are overpainted 
with red or yellow paint.  I also see visible 
fading of trace lines under brown paint on cels 
that I've acquired, probably indicating that they 
were displayed in a dealer's shop before being 
sold at auction.

These were inexpensive cels, so I'm not concerned 
so long as they are still attractive, which they 
will be for some time to come.  But when I framed 
a more expensive cel for my office, I found the 
fading so obvious after a year that I removed it 
from its frame and put the cel back in the closet 
to prevent further damage.  (Yes, I used UV 
resistant glass, for what it was worth...)

So to answer your main question: if you really 
care about their condition and look at them 
closely enough to watch for line fading, no, 
they are not safe, even with UV resistant 
glass on top.  

I have heard from friends who have framed cels 
and then put little curtains over the top to 
block the light.  That might work (and would give 
you the option of taking off the curtains when 
you invite a guest or significant other over). 

But I prefer to leave the cels in the dark and 
display the scanned images.  And, so doing, I 
have not seen any significant change in the trace 
lines on cels I've stored in the dark for as much 
as 4 years.