> that changes randomly
Moving the mouse pointer to middle of bottom edge of a screen will permanently move the Dock there. As far as I know, there is no way to disable this behavior. It's terrible.
For simultaneous multi-monitor, you're probably forced into using a full Dock replacement. There are a few options out there, but none have ever stuck with me personally.
If you go into System Preferences and disable "Displays have separate Spaces" it'll keep the dock and app switcher on your primary display.
I'm not a Spaces user so not sure what impact this has outside of the dock behaviour.