A couple of things:
The RandomEventHandler generally handles/dismisses randoms. No need to have your own method for it.
Also, never compare objects using == or != unless they are enum values (static and final, specific values). If you've already null checked them, there's no reason to compare them without .equals() like right here: randomEvent.getInteracting() != myPlayer()
This line:
getSettings().setRunning(getSettings().getRunEnergy() < 25 ? false : true);
can be more succinctly stated as:
getSettings().setRunning(getSettings().getRunEnergy() >= 25);
because it returns a boolean. There's no reason to restate something you already know.
while (myPlayer().isAnimating()) {
mouse.move(-1, -1);
}
^ Essentially the same thing, but please just say getMouse().moveOutsideScreen().
Also, the webwalker executes completely in one-go. This means that your code will probably only be utilized once before the walker is used and takes you to the correct destination.
In the onPaint() method, please don't define a new font each time. Create one font at the very beginning (because note that onPaint() is restored multiple times and very quickly - this takes up resources), and set the font at the beginning. No need for a new font object on each run.
(Graphics2D) graphics).setRenderingHints...
There is no need to pass in a type Graphics to this method because you know you're going to be passing in a Graphics2D. This means that there's also no need to cast.
spinG.setColor(new Color(255, 255, 255));
Same as the font thing.