Per MS-OXCEXT, the interoperability doc on how add-ins store stuff in Outlook, custom properties are stored as a JSON dictionary in a MAPI extended property (gory details at that link). That means you should be able to access them via Graph extended properties, you would just have to parse the value yourself.
Should be using extended properties and the "{type} {guid} Name {name}" format.
I don't see why not.
The answer isn't no, but I'll answer your follow up anyway :). Sure you can do this if you use the REST API from your add-in.