Welcome to RTA! Let me see if I can help you with some of your questions.

1) If it were MY trip, I'd definitely plan on Muir Woods. I've been there twice before and would go again if the opportunity arises. You'll have others comment about the car rental bit, as I wouldn't have an answer. There are lots of other things to see/do in the SF area.

2) We left Yosemite in a storm one time. It was definitely an adventure. I'm sure others will chime in on this.

4) Four days in LA would be great, IF you have an idea of what you want to do. That's because it will be difficult to narrow it down. Theme parks: Universal Studios, Six Flags Magic Mountain, Disneyland, California Adventure and Knotts could each take ONE full day. Hollywood could take a day or two. If you want a day at the beach, that's available too....bearing in mind that our weather may not cooperate AND the water never gets superbly warm down this way like you'd think it would.

5) One day in San Diego ... well, we have a ton of things to keep you busy down this way!

6) The helicopter tour from Las Vegas to see "the Grand Canyon" is going to take you over the Indian-reservation west end of the Canyon...NOT the Grand Canyon National Park area. That's because the GCNP has a "no fly" rule, but the west end does not. Worthwhile? I'll let others answer that, as I've never done that. I'd prefer to drive down and see the Canyon itself.
As for a car in Las Vegas, no. The Strip has a trolley and plenty of buses and taxes, and at that time of the year, walking can be fun too.

Happy planning!

Donna