My 90 lesabre did the same thing. When it cut off after driving I sprayed water on the crank sensor and it started right back up. A buick mechanic told me to do this and this is how I found out the crank sensor was bad!
Yest, the Buick LeSabre from 1992-1994 is the same exact car, inside, outside, underside. Everything is identical, except say for the trim packages and options you get on them. Therefore, yes the cassette radio from a 1992 LeSabre will work in a 1994 LeSabre.