-> I'm trying to record on a cassette,a distant FM station at 
-> 89.3 Mhz  located between 2 strong stations.I'm using
-> a radio with a collapsable whip antenna 23" high.
->   Anyone have an idea on how to add to the antenna to 
-> make the signal stronger?

You can go to an outside FM antenna. One using Coax would be
perferable(more noise rejection). Then on the radio end just clip the
center conductor of the coax to the tip of the collapsable whip(better
if it is only extended enough to clip onto) and the shield to the radio
chassis ground.

  
-> I have a Bearcat Scanner and with the transition of Emergency
-> radio to 800 Mhz,I was wondering if I could get a FM crystal
-> for 89.3 Mhz.A shop owner said that the crystal would cost
-> a lot and the scanner wouldn't work in this FM range.
-> Is this correct?           

He is correct. FM radio is a Wide band signal and reception would be
unsatisfactory on a Narrow Band FM scanner
  
-> I have a Rhapsosy Multiband receiver with a 6 " dipole
-> on top that doesn't pick it up.It has an jack for a 
-> remote antenna but I haven't had any luck with varying
-> lengths of wire,with no luck.Could this be made to work?

When talking about higher frequency signals(VHF-Low and higher) a Tuned
antenna becomes more important. Try using a Discone or another
wideband(Create makes several Yagis) type of antenna. 
The discone has basicly NO gain so it may not help much on very week
signals. The Yagi does have gain but they are more expensive.
If one is interested in FM broadcast DX only a good outdoor FM
antenna(the Longer the stick the better) works. 
And or even better reception you can stack 4 of them in a Quad
configuration using a matching harness.
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