OBD2 scan reveals unexpected engine problems?

Ken, thanks for your response. In researching the problem, I found several additional parts to the EGR valve-- presumably bought separately.

(1) EGR solenoid
(2) EGR sensor

This information comes from a phone chat with an auto parts rep, so I am not sure how much is accurate. In general, should I look further into these items? Ordering them locally may be more difficult, but Rock Auto may stock them.

How much of a hazard is posed by driving the car for a few days' of local trips with the old (and suspected defective) EGR valve still in place, pending arrival and installation of the new EGR valve?

The P0404 and P1404 codes appeared when I asked my local O'Reilly's to scan the system for errors, if any. Unfortunately, I had not done regular scans before that date, so the first (but unnoticed) code appearance can be only guessed to have been two months ago.

Although I would like to clean the original EGR valve, and actually loosened the valve to invert it for overnight "soaking" in brake cleaner spray, the next step is to pry the silver EGR mating gasket loose from the throttle body. If that gasket breaks or crumbles, that makes the situation worse, since I cannot use the original but broken gasket.

In this car engine, the EGR valve appears stuck closed-- when I start and run the engine to warm up, exhaust smell enters the cabin. Trying to understand the EGR system, the oxygen sensor tells the BCM computer the engine is ready to receive partially-burned exhaust gases, and the computer diverts some of the gases into the EGR. Which is stuck in the closed position, despite the computer's order to open for exhaust gases. That closed position explains the exhaust smell, but doesn't it also introduce the possibility the computer has switched to a leaner mixture, to accommodate the exhaust gas it "believes" are being diverted into the cylinders? And that means my stuck EGR is actually running my engine hotter and leaner. What damage could this introduce?

More information.
This afternoon, I attempted to remove, disassemble and scrub-clean the EGR, hoping clogged passages are the only problem. Unfortunately, I could not devise a way to take apart the EGR for a more thorough cleaning than simply squirting throttle body cleaner into both passages. Is it possible to disassemble an EGR for this GM engine? I found one TORX-type screw on the bottom-center, which seemed to be spring-loaded, but which simply rotated, and did not unscrew. And where two bolts appeared to pass through the EGR body, there was no visible opening for a nut or bolt head on either side of the body.
This EGR is the electronic type, with only a five-pin connector inserted into its top portion, and no other lines or connectors.

Here is a multi-view graphic for the part:

https://www.rockauto.com/en/moreinfo.php?pk=6698424&cc=1303287&pt=4968&jsn=9

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For better or worse, I have decided to do what most people do-- buy a new EGR valve. There are too many factors to control, especially since the car has an undocumented history, to spend more time experimenting with a used, questionable valve.

Thanks for the discussion of options !

Ken, in attempting to understand more of the EGR system, does this explanation of my EGR symptoms make sense?

In this car engine, the oxygen sensor tells the PCM computer the engine is ready to receive partially burned exhaust gases, and the computer diverts some of the gases toward the EGR. The EGR, however, seems stuck in its closed position, despite the computer's order to open for exhaust gases. That closed position explains an exhaust smell in the cabin, but it also means the computer has switched to a leaner mixture, to accommodate the exhaust gas volume it "believes" is being diverted into the cylinders.
And that means my stuck EGR is actually running my engine hotter and leaner.

This afternoon, I got the EGR, and plan to install it tomorrow.
Need your opinion on whether to use the stamped metal gasket which came with the part, or use an exact-fit, layered asbestos fabric (?) Gasket for the same part, which I ordered separately, in case the EGR did not come with a gasket. The layered, fabric gasket is the more conventional kind of gasket, and may provide a better seal under extreme heat.

Ken,
After installation of the EGR, an OBD2 system scan (O'Reilly's) showed no primary diagnostic trouble codes, which is good news..
Now, I am puzzled-- if I have not installed the spark plugs and wires, yet, how could the P0304 code for "misfire on cylinder 4" simply disappear?

If exhaust gases can leak from the EGR, could that explain occasional whiffs of exhaust gas in the cabin, too?

(After EGR replacement, I have not detected any exhaust gas smells-- so far.)

Ken, now I understand what you meant by "leaking from the EGR". The EGR, itself, does not leak to the outside, but fails properly to open or close on computer signal. That introduces an improper fuel/air volume into the nearest cylinder.

Yes, Joe, I have been able to resolve the codes issue for my Buick 98.

Earlier, I had received two EBD2 warning codes-- P0404 for an EGR
valve "open position performance" and P1404 "closed position
performance" and one EBD2 code P0304 for "cylinder 4 misfire
detected".

After installing a new GM-brand EGR from RockAuto, all codes simply
disappeared, including the P0304 "cylinder 4 misfire" Of course, I have
not operated the car much since the EGR installation, so the "Check
Engine" light might reappear.

My problems with this car arrive dramatically, and more or less
unexpectedly, because the wife of the person who sold the car to me
simply had tossed out all the services documentation over the years,
so, I have to guess what items will malfunction next.

The car has 252k miles, but was well-maintained by a professional
shop, so that offers some relief.

The car was received without the passenger side wheel well inner
sleeve, which protects the accessory belt and pulleys from splashed
water and road debris. I know the number of the OEM part for the
sleeve, but no one' has it. (I have not searched all the junkyards.)
To resolve that problem at least, for now I am searching for a
robust, waterproof material to use for a hand-made sleeve.

Any ideas?