Yes you can book a cruise. Call Member Services (option3) and then choose Option 2 and then Option 1. I am not sure about the availability, but if you are not picky about dates and flexible on cabin sizes, you will probably get something.
The point price does not change. It is a pre-negotiated amount - no specials for last minute cruisers.
As for single occupancy. I am not sure about point price, but the cash price runs somewhere around 1 1/2 times the "per person rate based on dbl occupancy." If you call and find out, report back and let us know.