Is Romanov under contract in the KHL next season? How soon can MTL bring him over to start getting experience on NA ice?

First off I never realized how had this info can be to find! From what I can tell he is under contract for one more year in the KHL as one of the more reputable sites I frequent puts his expiry date after next season but I don't say that with 100% confidence. Getting him on North American ice and not necessarily in the NHL is the big point here as the tighter playing surface and different angels take a bit of getting used to.

His contract with CSKA runs until the end of the 19-20 season. I’d expect him to be in North America in 20-21. During the World Juniors he said that he will be in Montreal in 2020.

2020-2021 is the earliest he can come. Depending on what Bergevin thinks is best, he will be here then.

Not entirely sure here, but I seem to have read somewhere that in extreme situations, a player can buy out his own contract in the KHL (not sure of the terms, or if even possible). Can someone else verify this?

Yes, but per NHL/KHL Agreements, Montreal is not allowed to help. If Montreal wants to get him over here earlier, Romanov has to hit the Lotto