No. It's valet parking. Think it's about $23 a night
No. They charge for the parking. $15 a $17 per night if I remember correctly.
No. We paid $25 per day (August 2018)
No, only valet parking.
Public Parking is also an option. Pull up Google maps and you will find a lot that is right next door. No wait for the valet guy, no tipping, and I'll bet it would work out to a lower cost. Did I do that? No, I used the valet most the time. Only jam I had was when we first showed up, the valet curb was packed and I had to roll around the block at rush hour and that took 20 min; if I did not have a load of bags to dump I would have self parked.
Get an answer from Hotel Carmel staff and past guests.