Question

So is the damage dealt going to be 50% of what the user of the move that Me First is targetting was going to do, or is it 50% of the base power of the move? For example, would the damage change with Me First if a 200 (random numbers) Attack Alakazam used Psychic and a 100 Attack Alakazam used Psychic?

Answer 1

User goes first with the opponent's attack at 1.5x power.

http://pokemondb.net/move/me-first

The user copies the move that the target has selected in that turn and uses that move itself, with the power boosted by 50%. Me First will fail if the target moves before the user, or if the target uses a non-damaging attack. If Me First is used on the recharge turn of a move that requires the user to forfeit a turn after its use, then Me First will copy said attack regardless. This move cannot be blocked by Substitute.

http://www.smogon.com/bw/moves/me_first

So, it is 50% of the Base Power of the move.