I think Rob will manage to be available. He only has the Bong Jong Ho film lined up, which is a WB production and I doubt it'll take that long to shoot, and Colin in an interview implied that the Penguin show would shoot in a span of 6 months. If let's say Batman only appears in 3 episodes out of the 8 episode season, that leaves enough room for Rob to appear.
And given that the US government declared martial law, I think it's pretty likely they'll stay around a bit for all the rescue efforts, but even with the whole "hope speech", Batman's priority still has to be the mob because again, it was not going after Falcone and the corrupt politicians which caused this mess on the first place. He cannot allow Falcone 2.0 to exist. Obviously Penguin will end up being the kingpin and outsmarting Batman, but Batman needs to make an active effort to stop that. After everything that happened with Falcone in this film I just don't think there's any justification that'd cut it.