Yes, Micro.blog themes are just Hugo themes so you can develop them locally. Micro.blog provides some extra stuff so you might have to add things to your local configuration file to simulate the Micro.blog build environment. This config.json file is a good starting point.
Also, make sure your local Hugo version is the same as your Micro.blog blog’s. Take a look at the Design page to see which one you’re running.
How does Micro.blog even work? and Plug-in editing changes are good reads.
See the links above.
That’s up to you, both approaches work. When I develop plug-ins I do most work on my local machine (and push to GitHub) in combination with minor changes and experiments directly on Micro.blog. (Often on my test blog to spare my main blog.)
Updated answer based on feedback from Manton below: yes! And that’s a great idea because Micro.blog won’t merge YAML and TOML files.