You can get 15-20% off without much delay (if any) pretty consistently. Transactions stay private so far as significant info is concerned (they have a nice chart showing which parties have which information related to you and the transaction on their site, or used to). Which reminds me, I need to order a wifi extender... heading over there now!
What is the minimum discount that a person can get for a purchase at amazon through purse.io in the start ?
You set your own discount; of course, setting a high discount means it will take longer before anyone is interested in taking you up on your offer, if ever. They used to have a guarantee that a discount less than 10% would be filled within a day, but I don't know if that's still operative.
Regarding security, I was one of the people that was burned (apparently) by fraudulent buyers; Amazon started canceling a bunch of gift cards I'd bought via Purse without warning. Amazon was very difficult to deal with, but Purse ended up giving me a total refund on my BTC. They've been very good to work with in my experience.
Coindesk has an article up right now about how Purse has opened a bricks-and-mortar store in San Francisco, offering items at a 10% discount from Amazon prices. The catch is they only accept bitcoin! That inspires confidence, since they can't hide out as an anonymous internet entity while operating a physical store. Scammers might try to utilize their service, but I'm pretty comfortable the Purse team itself is on the up-and-up.