The game is centered around wifom for when the mafia should use their redirects and when Cops should investigate (if at all). The N2 suicide in the event of no Cop investigations is there as a way to break the no investigate at all strategy (which might probably be best) and spur the Cops into tentative action. The double-kill rule is there to prevent the game from being broken via massclaim and also give the Cops a dilemma about when/how to roleclaim (if at all), as it may setup a double-kill. This rule also allows mafia to potentially fakeclaim Cop while both are alive.
Personally I think it's likely that 1 or 2 Cops will/should investigate N1, so I think mafia's best play is to redirect twice on N1 and to put town in even numbers on D2 and/or hopefully use up the PGO shot/frame someone. It's risky for Cops to not investigate on N1, because if the other Cop doesn't investigate also and either is NK'ed, the last Cop is forced to investigate on N2 at the risk of the Scared Loner suiciding. This prevents the Cop from claiming D2 to be innocent/force a 50-50, as being mislynched in a 50/50 creates a Scared Loner suicide OR being forced to investigate N2 while mafia know who the Cop is, is very bad if they actually do still have a redirect left.
However, if the Cops think redirecting N1 is a likely mafia play, investigating N2 is a better strategy despite being forced to investigate then. And so on and so forth with the wifom.
The "solo-mafia can redirect AND kill in one night rule" is there in the event of a D1 mafia lynch, and gives him an opportunity to get back in the game on N1 with a potential for 2 kills OR a clever frame, assuming Cops will claim a guilty and town will be convinced enough it's not tainted evidence.
Whether or not a Cop actually comes forward and claims information will be an interesting dynamic as mafia can conceivably fakeclaim Cop with impunity on D2 if no Cops are dead by then. If a town Cop claims on D2, they risk opening up the double-NK possibility for scum, so what Cops' do with their information will be crucial.
I don't