"Up to 3"…..thoughts on if i can use this to move 0 power, essentially making is a 'after a char is killed, draw 1' …. ?

Text:
Response: After a character is killed, move up to 3 power from that character to another character controlled by the same player. Then, draw 1 card.

Generally speaking, when an effect says to "move" something, unless something physically changes places, the move is considered to be unsuccessful.

So while on the one hand, "up to 3" does include 0, moving "0" doesn't really result in successful movement. It is like kneeling a card that is already kneeling. So, since the move is unsuccessful, you will not get to "then" draw a card.