Sicily and Malta

Given the ferry terminal location at the southern tip of Sicily (Pozzalo), it really isn't a great option for you given the very short time you have and your location in Taormina (which is in the opposite direction and would take a substantial amount of time to get to). Take a short flight from Catania into Malta's Luqua Airport instead.

If you have only 3 full days in Malta, would you consider staying in Valetta instead? It's much better located, more atmospheric (it's like being in a movie set due to the fortifications, which are fascinating), easier and cheaper to get to from the airport, and more central to everything else (all the buses radiate from outside the walled gate and go all over the island). You could easily do without a car and just use the bus system. Be aware that you have to reserve spots at the Hypogeum because the site only allows a certain number of people at once for preservation reasons. With only three days, I'd spend most of the time in Valetta and take a side trip or two close by: Mdina is a real gem and the Three Cities are great as well.

If you're set on St. Paul's Bay, then I would try to see sites closer to there. Naxxar is a lovely, but small village. Mosta has the really interesting Mosta Dome; Comino has beautiful waters; and Gozo is interesting in its own right (you can get there by ferry). But three days is an awfully short time to take everything in. Even though the island is small, it still takes a while to get around. Some of the traffic jams are crazy, and the roads are often narrow. I would personally use the bus everywhere except Gozo (which is much more rural and free of cars).

Sicily- It looks like your hotel is down closer to the water than up in Taormina. I don’t know if you realized that. We took a gondola down to the beach from Taormina one day.
You drive up steep, curving roads to Taormina. Taormina is filled with lots of stairs, very verticle, but you have beautiful sweeping views of the water and land, including Mt. Etna.
Restaurants we enjoyed there were Nettuno and Nero d’Avola and we walked to both easily from our hotel
You would be able to visit Mt. Etna if it interests you.
Ortigia is wonderful, we recently spent a week there and loved it, but so are Valley of the Temples and Villa Romana Casale( mosaics.) I would put Valley of the Temples at the top of your list. Three days is barely enough to see anything in Sicily, two weeks is a good start. Why don’t you put all seven days together in either Sicily or Malta? You will spend a day traveling in the middle of your trip as it is. I haven’t been to Malta yet so can’t comment.

Even seven days would be terribly short for Sicily; you'd only be able to see part of the island. How about spending all seven days on Malta/Gozo?