I am glad that you made it work!
Now, I haven't really done any search for enemy AI yet, didn't need to. I am not sure about the 4 directions and the path finding though. The only true benefit by using it will be if you have obstacles. Otherwise, using events you will probably have more control around the enemy's movement.
This is a capx I had made for an other topic, the goal was for the enemy to move vertically until he line him self up with the player and then move towards him, in a Double Dragon fashion. You can get some info out of it that might help you build your own movement.
As for the attack, just make a distance comparison* (or use an invisible sprite that is bigger than the enemy's sprite and check for overlap) and when true, set an Instance variable "Attack" to true and create the necessary events for the enemy's attack.
*The distance comparison should look like this:
(System - Compare 2 values)
distance(Player.X, Player.Y, Enemy.X, Enemy.Y) < any number you want ----> Player set Boolean "Attack" to true
distance(Player.X, Player.Y, Enemy.X, Enemy.Y) > the same number as above ----> Player set Boolean "Attack" to false