If Rogue (Before gaining Ms. Marvel's powers) was slimed by Toad, and Gambit found her with the slime hardened to her face, would he be able to use his powers to charge the slime with kinetic energy and break it without causing Rogue harm?
As Marvel Universe explains, Rogue's near-invulnerability is a power she gained from Ms. Marvel.
After permanently absorbing the powers of Ms. Marvel, Rogue possessed an amalgamated mutant human/alien Kree physiology that granted her a degree of immunity to poisons, and a virtually indestructible body.
As such, without Ms. Marvel's powers, an explosion to her face would harm her (assuming she has not temporarily absorbed anyone else's defensive or healing powers).
Yes, as long as Gambit was smart about it. For example, if he made skin contact with her FIRST (hands, neck, etc.), he would transfer his immunity to his own powers. However, no skin contact, no more Rogue.