As I understand it, the very point of the sympathizer cards are to help out which ever side is loseing (any resource in red or not) at roughly the midle through the game (the sleeper agent phase). Keeping that in mind we might be able to answere the questions.
1a. Pure human + sympathizer + red resource
1b. Pure human + sympathizer + no red resource
2a. Hidden cylon + sympathizer + red resource
2b. Hidden cylon + sympathizer + no red resource
3a. Revealed cylon + give away sympathizer + red resource
3b. Revealed cylon + give away sympathizer + no red resource
4a. Revealed cylon + keep sympathizer + red resource
4b. Revealed cylon + keep sympathizer + no red resource
1a. Humans need a helping hand so sypathizer is a sleeper agent who decides to help the humans (he plays for the human team, but story vise he is a cylon). He is sent to the brig as to not give the humans to much help (humnas don't trust even friendly toasters).
1b. Cylons need help. The sympathizer is a human story vise but plays for the cylon team. As he is not actualy cylon his cylon actions are restricted (to not help the cylons to much).
2a. Needs to play the same as 1a to not give away the identity of the hiden cylon... But the the question remains, can he then reveal him self later? Kind of like a dubbel agent. I guess the answere is yes, even though the help for the humans is then thrown out the window... Strickly going by the rules it should work like this. The sympathizer card, once resolved is treated like a "You are not a cylon" card. And the remaining cylon card override all your not a cylon cards leaving you a cylon playing for the cylon team. And as such you are free to revela or stay hiden as you see fitt.
2b. Allso needs to play as 1b to protect the identity of the hidden cylon. So the player is a cylon possing as a human who sides with the cylons. He is then restricted in his cylon actions. He should then be able to use the resurectionship to give his unrevealed cylon card to an other player, or reveal him self to regain his full cylon powers.
3a and 3b. Nothing odd here. The person receiving the sympathizer card will be in situation 1ab or 2ab. The revealed cylon stays a revealed cylon.
4a. The rulez specificly says the card must be resolved right away. And they allso state that you "may choose" to give away the card. So keeping it is clearly an option... But now it gets contradictory. The rules say you are sent to the brig, but revealed cylons can't be sent to the brig right? The card is then treated as a you are not a cylon card, but you still have your revealed cylon card so you are still on the cylon team... The most logical thing to me would be to ignore the effects of the card should you keep it. So the only reason to keep it would be if you think you might risk sending an unrevealed cylon to the brig.
4b. Allso a bit contradictory. Does the effect of the card strip you of your full cylon powers? Seems odd... But then again, why the frak would you keep the card in this situation? Is there any enterpretation of the rulez that would give this option any valide strategic use?
To me it seems like the chooise to keep the sympathizer card as a revealed cylon is a bit of a mistake in the rules? Mabye the intent is that you must give it away?