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check to see if your car has had the ignition switch recall completed
One reason a 1998 Cadillac Deville would cut off while driving could be the fuel pump or the car is out of fuel. Another reason could be the spark plugs.
Low brake fluid in the master cylinder
You might want to have the CV joints checked. When bearings start to go out, they make a "clicking" or "rattling" noise while driving - especially while making turns.
Timing belts on these cars are usually replaced every 90K; you don't want to have a timing belt go while you are driving... :(
It is scared of something, is there an Escalade around? Seriously, shaking while driving could be wheel balancing or front end alignment. Shaking while at idle or what seems to be coming from the engine might be a motor mount.
Problem with the SRS. Seek professional help. Not a DIY repair.
My 1998 Accord V6 gets, 25mpg in city driving and 31mpg on the highway at 70mph.
Out of gas
Probably an issue with the parking brake switch.
AnswerYup, in most cases. Check the thermostat.
Ideally, a thermostat should be changed before it fails or begins to fail. Personally I would change it every five or six years or so, with normal driving.