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1. Is it possible to use COM to open and control 2 (or many more) separate instances of Origin at one time? (Not projects, since I know Origin can only support one project at once, but just separate Origin applications/windows)
You can create multiple instances of Application.
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2. If not, is it possible to open, edit and close an Origin object/application and then re-open a new one?
To save a project: https://www.originlab.com/doc/COM/Classes/Application/Save
To create a new project: https://www.originlab.com/doc/COM/Classes/Application/NewProject
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