It’s possible, anonymous, but it’s more likely that they simply see mimikyu as a baby pokémon to raise—a sort of replacement for their lost child. I realize that sounds terrible, but what I mean to say is that they likely understand perfectly that this mimikyu is not related to them (it most likely doesn’t have the scent or electrical signatures of a pichu anyway), but they nonetheless see mimikyu’s presence as a moment of hope for them. They’re taking comfort in the possibility that they may be able to raise a child of their own after all, even if it’s not technically theirs.
As for your other question, certainly, anonymous. Although care for a mimikyu is vastly different from care for a pichu or even a pikachu, your raichu should be able to figure it out based on instinct and perhaps a little guidance from you. Do your research on how to care for a mimikyu (I’m afraid that while I can offer guidance on the matter, that would make this post far longer than it needs to be) and nudge your raichu along whenever it seems like they aren’t quite sure what to do in order to raise their adopted child.
Best of luck to you and the new addition to your family, anonymous!