Superman may continue his movement, but if he moves into another square adjacent to that character his movement will end because of Plasticity. (At least that's how it would work at the moment.)

That's how I ruled it because supes had already broken away from the character.
I was not 100% sure though

Right. Plasticity causes the character's movement to stop when they enter a square adjacent. Superman is already in a square adjacent to Ultraguy when Ultraguy gains Plasticity: he isn't entering the square, so the Plasticity will have no effect at that point. Only if he moves into another adjacent square will Plasticity trigger and end his movement.

Pretty much: the attack has to occur during movement, but it can be in the last square of movement as long as something external isn't the cause of the movement ending. So, Ultraguy can attack from his last square of movement, or can simply choose to stop in the square he attacks from: in those cases you're saying "I'm moving into this square and making an attack, and then ending my movement." But if some game effect like Plasticity or entering Hindering forces his movement to end he cannot: in those cases it's "I'm moving into this square" and something else says "and now you stop moving" before the attack can occur.

Generally speaking, my (and NecroMagus') direction to the deputies is to provide assistance when it is needed. If a thread, like this one, has the ruling clearly answered and explained, then someone saying "It's not right unless an Orange says so" is not something they should be spending their time on.