A few related questions here.

1. Number (and type, i.e. Imperial vs Merc) of reserved and open groups is known to the Rebel players, right?

2. Number of "Keep this card secret / discard" agenda cards is kept hidden from Rebel players?

3. If 2. is true, then number of remaining Influence points the Imperial player has is also kept secret? (because if Imperial player has to announce "I have spent 2 Influence" and did not put any Side Mission, Forced Mission or Ongoing cards into play, that gives away the fact that he has purchased two "discard" agenda cards (since they always cost 1 Influence).

Thanks!

1.yes.

2.no, it's open information.

3.gaining influence is open information, and spending influence seems to be open information.

To purchase Agenda cards, the Imperial player shuffles the Agenda deck and secretly draws four of them.
He may purchase any of these cards by spending influence equal to the cards' costs.
* The Imperial player does not show his drawn Agenda cards to the heroes. Any cards he does not
purchase are shuffled back into the deck without being revealed.
* Most Agenda cards are immediately read aloud and resolved when purchased. The only exception is if
the card instructs the player to "keep this card secret." The Imperial player keeps the card and resolves
the effect when he plays it.

I guess my confusion was in "keep this card secret"... I wasn't sure if it meant to keep the card face down (but still revealing the fact that it was purchased) or hidden from the Rebels.

It means that you keep the contents on the face of the card secret.

not the existence of the card itself...