There are some standard UI components that can display multiple screens.
If they're not suitable, you can roll your own solution by including multiple full-screen SVG elements in your .gui file, and controlling their visibility using the CSS display attribute (with values of 'inline' or 'none').
When an app is restarted, all variables are initialised from scratch (ie, they don't retain the values they had previously). The best way to retain settings on the watch is to save a local copy to storage. When your app restarts, load any previously-saved settings from storage. Overwrite them if new settings are subsequently received from the companion.
The official documentation is a bit light-on for details. More information is available in the section on visual styles(!).