Try this for event 4:
NOT Player: Animation "Animation 2" Is playing
NOT Player: Animation "Animation 1" is playing
Player is walking
action: Set animation to "Animation 1"
Because, this:
NOT Player: Animation "Animation 2" Is playing
Player is walking
action: Set animation to "Animation 1"
is going to constantly set the animation to Animation 1, starting from its first frame, no matter whether Animation 1 is playing already or not.
Basically, you want to check that the animation you intend to play is not playing already.
At least that's how I understand it, and that is how I am doing it.
Likewise for your next event, you will probably want:
NOT Player: Animation "Animation 2" is playing
NOT Player: Animation "Default" is playing
NOT Player is walking
action: Set animation to "Default"
I think that might be what Mipey meant.
You may want to do similarly for event 6, On key X pressed, depending on what your animation does.