1997 Saturn SL1 EGR System fault....

yes u should be fine driving driving it untill u have it looked at but if it starts sticking then u could have the car stalling so dont wait forever to have it looked at.

What is the likely problem of the ones described and about how much to fix?

which code do u have there are several egr codes?but most of time its a sticking egr from carbon build up if ur handy with tools u could take it off push the plunger down slowly till it bottoms and see if it doesnt return its spring loaded.u could even get a good can of carb spray and spray in it there to clean up the carbon.they even have stuff that eats up the carbon better then that if u went to like a napa auto or something and ask them.let me know what code u have and what u find.

I think the code is P0404

With that code I would try cleaning the egr like I said and have autozone clear the code and see if it comes back worth a try also when u have the egr off start the car for like 5 seconds then turn it off this will help blow carbon out of the egr port that could make the egr stick.when it starts the idle should go up if it idles normally then u have a clogged egr port let me know what u find.