I need to know how to wire 2 switches to one instead, so I can power on the screen and the system at once?
Diagrams would be a plus, but its okay if not.

If they're on two separate batteries, you need a double pole single throw switch. (Basically two switches in the same case with the same lever.)

If you're only using one battery, a regular on/off toggle switch will work if you put it before the power splits to the two components.

A diagram would help, but basically for 2 batteries, I would hook the power switches to one switch?
Or not? Am I getting this the wrong way? Just want to know :/

Are the batteries completely independent, or are they tied directly together in series or parallel?