'92 Buick Regal, 47k miles, alwaya reliable, but yesterday shut off engine when warm, then restarted, car backfired and blew off hose to brake booster. Would not restart immediately. When did rest

it flooded. step on the gas pedal fully and crank the engine; that forces it to go into a clear flood mode by turning off the injectors. it may take a little while, but it will start.

look to see if a hose blew off like the intake or a vacuum line

If the engine died you would loose power assist steering and power assist brakes. I have to think it was an electrical power failure somewhere.
Will it start up and idle now ?

check wheel bearings as well as rear brakes and baering

Any engine machine shop should be able to repair it, unless there is block damage. But is a 89 Buick worth the $2-3000 to replace the engine? Unless its in 100 percent perfect condition, or you really love it that much. I would recommend a JASPER rebuilt engine. 3 yr/ 100k mile warranty.

How warm does it get? The computer won't turn them on unless the coolant temp gets to 235

It is most likely a crank sensor!!!!!!! i am 99.9999% positive that this is the culprit. I am a mechanic and this is the first thing i would check with your description.

egr valve is not opening up when the engine reaches it normal operating temperture

ok its one of two things you need to check when it cuts off if you have spark or fuel if you lose fuel pressure replace pump it gets hot and makes noise like its running but its not pumping fuel and if you lose spark you need to replace ignition control module has a hair line crack in it and when gets hot the crack expands and loses contact and wala no spark

sounds like the ignition module but it could be a fuel problem