I want to try to understand how these work. Looking at Clone Captain Zak, he gets a token on him to start with and you can exhaust him to give yourself an extra die. Then you can spend the token that's on him to refresh the card. I understand that bit. Once his 'reservoir' of tokens is empty can you refill it by sending tokens over from elsewhere or by turning a CF dial in to a token?

Can the token that he carries be used for any other purpose, such as to reroll 1 die on the ship he's on? Does his token count towards the limit of tokens the ship can carry?

When do these cards get refreshed? If I have a ship with Munitions Resupply on it, I exhaust it on turn 1 to hand out tokens. On turn 2 I draw an engineering dial (for example) and I can use that dial to un-exhaust Munitions Resupply? Does that un-exhausting happen at that point and can I then immediately use the Munitions Resupply to hand out more tokens?

You ordinarily refresh those "pay to refresh" cards with Tokens on the Ship in question. You can use the token on the card, when the card says so.

Tokens on the Card are NOT tokens on the Ship, and can't be used for any other purpose other than what is listed on the Card. Thus they don't count for the limit or anything like that.

Un-Exhausting of cards is only ever at the Status Phase . For free if they regularly refresh, or with cost if they have a cost. That cost would be a token, so plan ahead .