TL;DNR: Yes you can edit Geometry Nodes in the Modeling workspace. No you can't sync the same editor in two different workspaces so that both workspaces always show the same thing.
The manual section Window System Introduction is a good starting point for learning the names of the various parts of the Blender User Interface.
The simplest form of Blender has a single window that has a Top Bar that contains the various master menus and a collection of tabs for Workspaces.
To answer your first question, yes, you can change the layout of a given workspace. A Workspace is subdivided into areas. As you can see from the area manual section, you can change the layout; adding or removing areas, and moving the borders to make one area larger and another smaller. You can even split an area into two new areas or join two areas into a single area.
You can put any editor you want into a workspace by selecting it from the Editor Type menu, so yes you can have a Geometry Node Editor in the same workspace as a 3D Viewport editor.
What you can't do, is have an instance of an editor in one workspace exactly match an instance of the same editor in another workspace. The editor windows are separate from each other and (with the exception of the timeline indicator) there is no synchronizing.