The rules say that the rogue galaxy upgrades it's empire when it acquires resources through die rolls (since that's the section where the info is listed) it'll upgrade it's empire. I'd say that the rogue's culture track would stay where it is but you'd lose the culture still.
I would choose the rogue's special action in the order they occur in the rulebook, energy then culture, but that's just me.
The first reroll of each turn is free; thereafter, a reroll, of any unactivated dice, costs 1 energy
I would say this means that you can reroll as many unactivated as you want, and then if you want to reroll them again, it'll cost you another 1 energy. If you then choose to activate a die, then reroll the rest, it'll cost you another energy as well.