Not sure about the privacy of Presearch but their results are really good. A few times already I was searching for something I know existed out there and only Presearch was able to find it.
By "respect your privacy" I mean no personal data is collected. So as long as you are not putting personal details about yourself in the queries and use a VPN you can stay pretty anonymous while using the service.
Not sure about using visa gift cards, but there is Haveno DEX branded as RetoSwap which is a peer to peer exchange with many different payment methods available. https://retoswap.com/
They do, the website is just a portal to the network for exposure. Using the app is the real Bastyon.
https://github.com/pocketnetteam/pocketnet.gui/releases
or
https://bastyon.com/applications