Did anyone back in America know about Michael's marriage to Appolonia in Sicily?

In the film, this was never revealed. In the book, Kay is told by Michael Corleone's mother to forget about him, implying that Corleone was already married and would never return to the US. The family in the novel The Godfather is well aware of Michael's actions in Sicily.

Since the film leaves out Michael Corleone's revenge against the man who planted the bomb in the car which killed Apollonia it is clear that her death closes that thread of the tale.

In The Godfather 3, a wise and aged Michael Corleone shows a photo of Apollonia to his daughter Mary and his son Anthony saying

She was wonderful, beautiful. I loved her. And then she died. My trusted bodyguard planted a bomb in my car. She drove it before I did.

The idea behind this conversation was to convince Mary to stop her relationship with Vincent Mancini, the illegitimate son of Sonny Corleone and Lucy Mancini.

When they come... they come at what you love.

Kay knew. In the book, she sort of put the pieces together. Also, in Part 3, she sarcastically mentions the marriage when Michael tells her he never stopped thinking about her in Sicily.