When attacking a character with a move and attack action (charge, HSS, RS) and the character being attacks makes a Skrull, shape-change, etc. roll does the attacking character stay in the square he started in or the square he was attacking from?

For Charge and Running Shot, the movement is completed. There will be no more. If you can make any attack of the same type, you must do so, even if it means that you need to waste your object smacking the wall.

For HSS, the movement is not completed, but you must make an attack in that same square, if possible. You can continue moving after that. (If you can't make an attack from that square, you can keep moving, but you lose the attack.)