A good deal of this goes back to my belief that Tom gets a bad rap on the boards.

Just as Tom intuited the "secret" Neri regime, he also intuited that there would be an attempt on Michael's life...at Vito's funeral he matter of factly asks "Do you know how they're gonna come after you? And then..."I always thought it would be Clemenza."

As for Fredo, I believe Fredo contacted Tom from New York. Considering the Castro takeover and the escapes by Michael Fredo and Roth, Tom had to know something was up when Fredo called from NY, and being the non-Sicilian, he evaded Michael's questions about Fredo's whereabouts because in his heart he knew that Fredo was a dead man.
As for Connie, it is unclear that she knew what Fredo did to deserve to be killed, but by the time of III, it is clear she knew because when Michael tells her he went to confesion, the firt thing she talks about is Michael's greatest wrong -- fratricide. So she glosses it over with the fiction about "poor Fredo drowning."