Loaded questions…
First, yes, if you book a shore excursion through the cruise line, they are not suppose to leave you behind. I’ve seen them wait for sponsored excursions.
Recommended with GIG- We did the home cooking demo in Mykonos. I would highly recommend it. The hostess was entertaining, knowledgeable and made fantastic food. I didn’t think I liked Greek food, but the whole meal (and the wine) was fantastic. I’ve made her tzatziki several times and someday, I’ll make her Souvlaki. I’ll attach photos below.
Booking separately depends on the provider. Some pick up at the port. Some require a taxi or bus. Just make sure you get the arrival time correct on the information form.
I’m sorry I can’t help with Delos. We didn’t do that one.