1. Especially for first timers, the Westin Ferry is just so easy and convenient. I'd recommend that. It is more expensive but this is not a budget trip... Anyway, you'll want to come back, and then knowing more about how everything works you can debate if you want to try something new next time.
2. Dolphin Market is walkable and probably has most of what you'd need. Starfish is a bit bigger and has pre-ordering for pickup/delivery as well with enough notice. Can also pack stuff from home to save money. If you take the Westin ferry you basically don't lift your bags from the STT baggage claim until you're in your room (so heavy bags full of food not as big of a concern).
3. Depends on how many days you think you'll spend either beyond Cruz Bay or needing grocery trips. I find it's typically worth it for us to rent for the week for the flexibility and ability to go anywhere anytime.
4. There's not really a bad choice in restaurants. Try a bunch, check google/yelp for more info/ratings. Morgans Mango is one of the most popular and longest-established places I think.
5. I tell everyone to go to Lime Out (floating taco bar in Coral Bay); just a really cool experience and some incredible food and drinks. Good excuse to drive through the national park to get there and see the beaches and historic sites or hike a trail. Francis Bay is not as busy and near the Annaberg sugar mill ruins. Good chance to see turtles there, like Maho. We like hiking the Lind Point trail from Cruz Bay to Solomon Beach as well. Very peaceful since you can't drive there. Heard great things about Windmill Bar sunsets but haven't been myself.
Enjoy! I can't wait to go back at the end of the year.