Eek!
It's shocking to read such elementary observations, corrections that neither me nor the local bicycle shop that today performed a service spotted.
I removed the large allen-headed screw. A wall of grease confronted me. I suspect your observation about the screw on the left side of the head tube is correct — to lubricate the steering. I removed much excess from its joint with the front fork.
I full strip may well be worthwhile. Alas, I do not have the space and knowledge to accomplish this.
Is there free online source for a guide to complete this?