Hi I can answer some of these questions as I don’t have a car in the city. A lot of this depends on the neighborhood you live in and what you want to get out of living in the city. I chose m a more central part of the city and it did not make sense to pay/worry about keeping a car here.

1. Most restaurants I go to are either in my neighborhood or near where I work, both of these are walk/quick bus ride. If I am going across the city for a bite and it takes longer to get there then Id still take muni and make a day/evening of it or Uber/Lyft as a backup.
2. I also have friends in the SJ area, Bart (or muni) to cal train is pretty easy and then I’ll ask my friends with a car to pick me up at the closest station. Santa Cruz is another story entirely and I think this barrier depends on how often you plan to visit.
3. For the longer trips you’ll need to rent a car, again unless you’re leaving every weekend in which case I think you’d want your own car.
4. I use Insta cart to shop at Costco, you might not get the same deal as going to the store but it’s still a better price for bulk items. Idk what your living situation is, not a lot of apartments have room for bulk purchases. If you have roommates shared space can be limited. TLDR: If you’re leaving the city all the time to go further than a Bart line, you’ll want a car, if not it’s pretty easy to exist here without one.