I'm not sure how long it takes from Sanur to Besakih. Get a map from tourist office at the airport and from your hotel. Ask your hotel staff to make sure how long and how to find your way on the road.
For 4 persons I think a Toyota Kijang is a good car.
You'll have to climb many stairs to get to the Temple of Besakih. I don't know which one is higher but it might be like climbing the stairs at Batu Cave Temple in Malaysia.
Tirta Gangga is at the south-east, far from Besakih and Sanur. If you leave Sanur early, and Besakih in midday you might have time, but it will be a very long ride Sanur-Besakih-Tirta Gangga-Sanur. You might get very tired.
You can surf in Kuta. For snorkelling, Nusa Lembongan is closer to Bali than Gili Trawangan (which is closer to its main island Lombok). But if you have much time you can hop on a ferry to Lombok and try one of the Gilis. Better tell the ferry operator that you intend to go to the gili, so they can arrange the trip or give you directions on how to get there from Lombok.
Yes, it's also very far from Ubud to Tanah Lot. Tanah Lot is not that kind of beach to relax, bathe and the like. People go there for its view. It's rocky, and late in the afternoon when the tide comes the huge rock cliff where the temple is on will be surrounded by water.
I hope you'll have a smooth, fun and great vacation.