When branching a TFS team project, can you change the process template used by the new branch, to something else? For example, if the project template used for the original project was CMMI, when I branch the TFS team project, can I then make the new TFS team project use the Scrum process template?
You can't "branch" a team project. You can create an inherited process template.
However, you can't change an existing team project between the root-level process templates (Scrum, Agile, and CMMI).