Are number of cards in hand public knowledge?
While there's no specific rule governing this in the rulebook, the board gaming community as a whole seems to agree that the number of cards in a player's hand is public knowledge.

There are a lot of forum threads that reiterate this answer on both BGG and Fantasy Flight Games (here, here, and here, for starters). The basic reasoning for this is because some alien powers require that information to be public, such as the Mutant and the Genius. (And, if I remember correctly, one of the alternative win conditions for one of the alien races is to have more cards than the other players.)

Additionally, in the last link above, forum member Adam notes that the online game allows you to check the number of cards in a player's hand, although I haven't played it so I can't confirm whether that's true.