UPDATE: Sorry for delay folks. OK first Where's question #3 ? I guess I had it in there and took it out before posting and forgot to renumber.
Now remember the unit is at my son's house a couple of hours away so I don't get there often, but I can instruct him on what steps to take.
I took Patricio's advice and I have actually got some help from the manufacturer. They too said to clean it and they sent a free wrap-around filter for the entire bottom intake area.I haven't called them back since.
At this point the unit has been cleaned thoroughly several times. Burner/pilot/thermocouple assy and lower plate removed (exposing ceramic disk). Compressed air blown on top with extended angle nozzle, simultaneously shop vac sucking on bottom. No debris is coming out any more. It HAS to be cleaned by now. It will stay lit for about a 5-7 days at a time now. Simulating an air restriction, and wobbly flame, we wrapped a thick cloth all the way around the air intakes. Flame goes very orange (expected). BUT even after 5 seconds it doesn't go out. I don't think this is a starvation issue. But what do I know. I wish I could set a video camera up to watch the pilot and see what happens when it goes out.
I still am not completely confident the main burner is drawing the pilot away from the thermocouple far enough or for a long enough time to lower its output below 20 mv.
The unit is just about 10 years old, and at this point we are considering replacing it. I hate to throw a $60 pilot/TC/igniter at it if there is little chance that this is the issue. I'd rather put the $$ toward a new unit. I certainly don't want to replace the controller.
Any more suggestions on where to go with this?