What control do I have over monitors and resolution?

When you connect, you see the entire desktop of the remote computer, regardless of how many monitors it spans. You can use the parameter system to remote just a particular monitor if you wish.

By default, the desktop is automatically scaled. You can display it at actual size using the Scale to 100% button on the VNC Viewer toolbar, or for more control use the Properties dialog:

If you have an Enterprise subscription and are using VNC Server in Virtual Mode, you can specify multiple screen resolutions (geometries) for a virtual desktop and then cycle between them.