Thats not the way you lose copyrights or trademarks lol. I am amused by the lack of proper info about that. And no, they wont lift a finger, they will make a blind eye until they get a new publisher investing on it, unless they selfpublish of course but I cant see that happening by how bad things have been for them at NA with EME (publisher owned by BHS)
Yes you do. If you do not enforce your trademarks (not copyrights, I checked) you risk losing them. That's why Nintendo is so diligent going after anything that's at all Nintendo related.
And just because the server is located somewhere where their trademark laws aren't recognized doesn't mean they won't try. As long as you show you at least made a reasonable effort to defend them, your trademarks will continue to be recognized.