What is the working principle of a Gurney Flap?
Adding the flap to an existing airfoil increases the angle of attack of the airfoil - just draw a straight line from the leading edge to the trailing edge: after adding the flap, the trailing edge has moved down to the tip of flap. The line before and after resemble flat plates at different angles of attack.

The vortex in front of the flap is produced because the flow can't make the sharp right angle turn around the flap, it can't perfectly follow the geometry.

The increase in CLmax should come from an associated increase in effective camber.

Total drag consists of skin friction drag (mostly, for an airfoil that is just "thick") and pressure drag. Maybe the increase in effective camber changes the relative amounts of both, leading to a net decrease of drag.