Yes, they do.
They take it to you room, no worries
Yes they do. Will give you a ticket stub and will lock up your luggage in the back.
yup just ask. Most hotels will hold your baggage for up to a year
Yes. They will give you a tag and also tag your luggage if its before your check in they'll take it to your room. They did mine
Yes
Both, if needed. The day I checked in -- the day with the housekeeping delay -- they were holding everyone's luggage at the desk. Another time, they were doing so for people eho were checking out. So, no problems!
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