[flibbr]

 

[jackjack]

I know the wiki contains what you want but I don't know in what pages

[fpgaminer]

2) Given a public key, you can calculate the address.  Check this wiki page for instructions on how addresses are calculated from public keys.

1) Well, you can verify that a public key (a point) is on the secp256k1 curve (the elliptic curve used by Bitcoin).  That proves that a corresponding private key exists (but you don't know which one).  I don't have a reference off the top of my head for you, but Google can probably help.