What is Malta like on Sundays? Is everything (shops & restaurants) closed? That was the case when I was in Germany and Switzerland. If so, I'm thinking Sunday would be a good day to book tickets for Hypogeum, combine with Tarxien before/after, and Birgu Fort St. Angelo afterwards. Is that a good plan

Please advice.

I don't know about all of Malta, but Valetta is in my experience pretty quiet on a sunday. Many shops are closed, but restaurants etc are all open. Take the ferry to Sliema and you'll find it's much more lively there, more shops open etc.
Actually, Malta on a sunday is nice: traffic not that intense, everything kicks back a bit.