I believe they have a shettle, but definitely bouble check. If it is too eaely or too late, they can call a taxi for you, and it wonzt be free for you. Not sure if the travel to SFO, but I have taken their shettle from SJC.
Yes it does have ab airport shuttle. I think 07:00 - 21:00. Just confirm with them please.
No
If memory serves me right, the shuttle doesn't go to sjc
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