I like how cleanly Guided Object Removal highlights part of a photo. Can I copy the highlighted part and then paste it in another photo?
I don't think so. But you can with the Photomerge Compose Guided Edit found under the Photomerge tab:
Yes, Frank, your method works. But really all you are doing is using the Guided Edit to make a selection of an object. Surely, you can do exactly the same in Expert mode, using the available selection tools. I don't know of any difference between making an automatic selection in the Guided Edit and making it in Expert Mode.
I tend to use the Quick Selection brush. Or if I am working with a solid color e.g. a sky poking through branches of a tree, then I will use the Magic Wand Tool.