if the self is an illusion - all my relationships are illusion too? If the self is an illusion - of little importance - where does that leave my relationships?

All the people I know, have a relationship with this 'fake self' of mine -- so the relationships are groundless? an illusion also?
You are asking something like "If superman is fictional, what happens to his relationship with Lois Lane?".

In ultimate reality, relationships don't exit. It's just craving/clinging arising in the mind for seeing, hearing, smelling, touching etc.