Torpedo duomatic stuck in one gear because of too much grease. How to lubricate correctly?
A couple of months ago I did this exact overhaul and it has been running super smooth ever since. Can't comment on the longevity yet but here is the logic:

Bearings: standard bearing grease, oil is too thin and will result in increased bearing wear.

Brakes: "Bremsmantelfett" (brake grease) from Hanseline. Here you can probably get away with normal grease, but if you do a lot of braking (eg. hilly area) the grease can heat up and harden, so the more heat resistant the better. Don't grease the braking surfaces of course.

Gears: oil, this area is well contained so no chance of the oil running away and oil makes the gears change smoother.

Pawls: oil, you can also use grease or a mixture but be careful not to apply too much grease underneath them or they can stick down. Give them a good test before and make sure they are really springy.

Other mechanisms: grease oil mix, oil can run away and get places you don't want (brakes) but grease can be prone to hardening. A sticky oil can also work here.

Not sure about the plastic ring you mention but if it rubs against something wipe a bit of grease on it. In general anything that should slide should have some sort of grease or oil on it and choose oil vs grease based on how well it needs to stay put.