I've more or less been following the walkthrough for specific instructions, but it's completely contradictory here: it says something about curing two groups of adherents, except most of the people it lists as adherents are not the Bachelor's adherents.

Several of the people who ARE the bachelor's adherents are also dead, and could not have been saved because the main plot said they had to die (Eve Yahn and Petr, I think, unless he was just being really overdramatic).

I've got a half-dozen panacea and one powder but no idea who the hell I'm supposed to use them on in order to get some sort of letter that will move the plot forward. Not only that, but a lot of the people I've talked to aren't even suffering from the plague: am I literally just supposed to go around the town healing every single individual character I find, or what?

In order to get any ending except the worst one, you should make sure that at least your adherents are OK. Petr should be saved (did you say him "OK, die if you want" on day 10?)
If you want to achieve Burakh's or Klara's ending, you have to make sure another set of adherents is alive. Or maybe all of them.

Ah, ok. I tried to save all the adherents, but I guess I missed one -- I couldn't find Mishka, I guess. I ended up going with Klara's solution (SPOILERS, but, am I right in thinking that she sacrificed all the adults so the kids would live?), but does anything drastically change if I somehow find a way to go back and save everyone except the obviously dead people (I guess Petr isn't dead since I didn't get a bad ending, though Big Vlad seems to have died after I gave him up to Mother Keeper -- is that impossible to get around?)?

Mishka lives in a railway car. Look for it to the southeast of the station. It is marked on the map, by the way.