1) How should non-killing/non-converting 3rd parties be balanced? We know the standard 9-player game, 7-town, 2-scum setup... how about 10 players? Assuming no SK/cult, how different would a 6-3-1 setup be from a 7-2-1 or a 6-2-1-1? if non-cult/sk, how much does it matter which 3rd-parties are chosen?
I think the question to ask is what exactly the 3rd party is likely to do. If it's the "do something and disappear" kind of 3rd party then it's kindof like just not having that person at all. If it's "vote with scum at the end" then I tend to treat it something like having an additional half a mafia member (and one less townie, making it about 75% as bad as having another mafia member). If the third party is a jester (don't use jesters) then basically just write off one of the town's lynches as wasted.
7-2-1 and 6-2-1-1 both sound fine providing the role powers balance. If the first one had a survivor or other pro-mafia 3rd party the town would need a little bit more power than usual, and in the second I'd make one of the 3rd parties have a vaguely pro-town or at least neutral wincon ("find and eliminate a mafia member", "protect a townie", "identify a certain role" or whatever) because otherwise town could lose the majority on day 2.
In a recent 10-p game, there were two scum, no sk/cult, and one 3rd-party flipped brother-to-a-townie. At the time, I felt justified in the assumption that there would be another 3rd-party, since the brother-to-townie thing made it seem (to my scummy eyes) favourable to town... was this assumption justified? Is a brother-to-townie in this scenario a 7½-2-½? Would a survivor (instead-of or in-addition-to) make it more/less balanced or different? How about a lyncher-of-town or brother-to-scum?
I'd say it's pretty much balanced just looking at the numbers. Disregarding roles town had 4 lynches in which to hit 2 mafia members, which is pretty standard, and had a guy who wasn't entirely sure if he was town as a distraction. However, I understand that Roguelike Mafia has lots of powerroles flying around, which is virtually always bad for scum. Maybe the setups should be a bit more scum inclined than normal to make up for that, an anti-town 3rd party might've helped since 3 scum would be overpowered.
Importantly: Would you choose/change these or their targets manually, or let the dice roll for them?
You mean with a lyncher or brother? There's quite a big difference in terms of balance based on which way it goes so I'd first choose manually the alignment that they're going after then probably assign a random person on that team (although if you want them to go after a key role/ not key role then there's no problem with that). You could also make it completely random and tweak the rest of the setup to compensate afterwards.
2) Say there are 10-players, would your choice of 3rd-parties numbers/alignments change in a PMs-allowed game, like paranormal, as opposed to a no-PMs-allowed game like most others?
For me, PMs are mostly useful for two things:
1) Talking to people you know are on your side due to inspections
2) 3rd party shenanigans.
The first is the more likely gamebreaker, I'd say, and would have a large effect on the setup. It can make the scum suddenly unable to lie or turn a cop into a kind of mason recruiter.
The second I'd say is only pro-certain 3rd parties - specifically, ones who are potentially beneficial to some players but who wouldn't want to reveal that to everyone. Being able to contact the mafia via PM is useful for a survivor or something like the Xeno from Paranormal. Most of these are lategame developments, though, and not too important to balance, however, for things like brother or guardian angels it completely changes the mechanics of the role.
If I'm a brother to a player, regardless of alignment, I can't think of a good reason not to eventually send them a PM letting them know; even if they would be guarded against the chance of a fakeclaim, it'd have a strong effect on the day play, yes?
I'd send them a PM immediately. I would make it clear I do not expect them to trust me in any way, and that I will not ask of them anything, but I'd claim my full role and say that they can instruct me to do whatever they wish (as long as it isn't stupid). This way you know for certain that you're helping the right team, and the person you're brother too has nothing to lose in telling you what to do even if they don't trust you. The only potential issue is someone being confused as to why you're doing it and raising the alarm in the main thread to try and get you lynched, but if you explain what you're doing well enough that shouldn't happen.
This does completely change how the role works - it's now basically an extra mafia member or townie (and if it's a townie they have a one-way mason link). That makes it a lot stronger.
3) if no 3rd parties in a 10-p game, is 8-2 balanced? or 7-3?
8-2 is still 4 lynches for 2 mafia members. The difference is there'll be an extra night... so as long as that extra night isn't going to cripple the mafia with inspections it should be fine. One key difference I guess is that the town only needs to stop one kill in order to get an extra lynch, so you'd want to be more careful in handing out kill blockers. Equally vigilantes can get effectively a free shot (IE they can shoot someone without taking away town lynches) so they'll be stronger too.
7-3 would have to be a very town friendly gametype. The town can only lynch incorrectly once, and they need to hit 3 mafia members.
4) How would these balance considerations change in a role-heavy game? (not Paranormal, where roles, SK/cult/Jester/others are distinct enough, but in general role-heavy or BYOR-types?)
Role heavy games are anti-scum unless you give the scum serious trickster powers. In that case you'd probably want to err on the side of pro-scum (9-3-1 for town-mafia-anti-town 3rd party seems to have emerged as a pretty good balance for BYORs).