As far as I know, Amazon private sales work like Ebay. Your money goes directly to the seller. The seller sends the goods directly to you. If Amazon get's some sort of percentage of the sale, that is something the seller has to deal with.
I wouldn't worry about anything. Sometimes those private sellers get lazy. It wouldn't be unusual if you waited up to a month to finally receive your goods, but the average wait is probably only 5-10 days.
The seller probably sent you an estimate about how long it would take to ship. I'm usually nice and won't even email them until it's been 3 days past the date they said, then I start harassing them