I can tell you that a vinegar bath definitely makes an immediate, noticeable improvement in a tired old cat. It's not like new again, but it's better. Doesn't seem to perk it up for too long, though. I suspect that wash coat flattening is a much bigger factor in performance decline than mineral depositation.Good questions, and hard to answer.
1. I'm not sure that water is the main vehicle for mineral movement. Smoke (i.e. nanoparticles containing organic molecules - and more) likely contains much too. I would not be surprised if that carrier contains more minerals, as I think there is not much steam (small droplets of water) - it'll almost all be water vapor: given the relative humidity in the firebox the stability of steam will be negligible.
2. Catalyst poisoning is quite often related to compounds containing sulphur (and similar elements). Sulphur is a common "linker" of organic compounds to precious metal atoms (i.e. the active part of catalysts).
3. I am not convinced the acid bath removes minerals. After they have been there, at high T, a mild acid as vinegar won't really do much to minerals I think. See #2 for a possible reason why this works.
I do note that I am fairly knowledgeable in this area but would submit to people that actually have data, rather than the (well-informed) speculation above...