I don't know about immediately. Even Ryujinx, another established Switch emulator that rivals Yuzu and used to be more popular than it, is still up with no news of an incoming lawsuit. This takedown will definitely lessen the number of people who'd want to contribute to the project, but I'm guessing it'll return back to normal as the Switch is discontinued and Nintendo starts losing interest in defending the system.

Could depend. If the next gen console is a Wii > Gamecube type situation, it may be that Yuzu could run games for it with minimal modification, just like how Dolphin can play Gamecube games. That would keep nintendo/their lawyers interested most likely.