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Is it possible for me to have a material preview window here in the space highlighted in the photo?
If not, is it possible to put one in the same spot as the UV editor window, and have them interchangeable with a click, like you would have tabs in a browser?
It is not possible to carve out a corner of a window that way, no. However, you can quickly toggle between two editors by hitting Shift and the appropriate 'function' key.
If you click the icon at the upper left of an area, it opens a menu that allows you to switch to a different editor. To the right of each editor you see 'Shift Fnn' where 'nn' is some number. 'Fnn' means hit the function key of that number.
So instead of a click Shift–F10 to pick the UV editor.
But what do you mean by "material preview"? If you mean viewing your object in Material preview mode, that's already in the window above the UV editor in your screenshot. If you mean the preview in the materials window, simply select the material tab in the outliner
EDIT: From your comment on my question.
"Material Preview" is something visible in the Properties editor's Material Properties tab. The preview panel is closed by default so you have to open the panel by clicking on the arrowhead:
The function key shortcut for the Properties Editor is Shift–F17 but a preview will only show in that Material Preview panel if you have a material selected and that requires that you have an object selected in the 3D viewport. (You don't in your screenshot.)
You can't limit the view to just the material preview, but you can create a Properties Editor window and size it to expose just that information.
Unfortunately that's as close as you can get to what you'd like.
Mostly we settle for looking at the material preview in the properties editor window that's usually open on the lower right in the default Layout view.
