How does that work? Do you just hope no one buys the car in the meantime? Or will the dealer let you store it with them?

Most (all?) dealers in California offer some kind of 24/48 hour insurance for you to legally drive home. The prices are sort of ridiculous when compared to normal car insurance ($50-$100 for a couple days of coverage IIRC), but thats just a function of the risk profile and the fixed underwriting costs of a short policy.

You can drive a car home without insurance. A quick google suggests californias grace period is 30 days.

It may be allowed, but who pays in case of an accident?

Your prior insurance covers you for a while