A Few Questions Regarding Secure E-mail, OSes, Bitcoins, and Web Search Engines

1. Which e-mail is the most private, who also encrypts the incoming messages? It can be invite-only, if necessary.
2. Which search engine is the most private, with it's own web crawler, no logs, and non-US-based?
3. Which OS is the most secure - which is fairly easy, or at least has a guide, for an expert Windows user - that can be configured to support HP hardware, Bitcoin wallets, Tor and VPNs?
4. Can you buy Bitcoins anonymously if you are in the US? How would I do that? Would finding a service that allows WalMart gift cards be possible? What other payment methods can I use anonymously, other than cash?
   

Any help is greatly appreciated.