So the character moves correctly and mirrors, but animations are not playing? Could you re-upload the changed file? In the previous version it couldn't even move properly with the touchpad.
EDIT: Actually, no need. The problem is that your two groups (Player Movement and TouchPad) are clashing. When no keys are pressed, your events 21-28 reset animation to "Idle" on every tick.
Since you have more than one way to control the character, the best solution would be creating a separate group that will manage animations, not based on control method, but based on 8direction moving angle.
Something like this: