1. you wallet is stored in your browser in an encrypted form - if you come back with the same browser, you only need to provide the passphrase to unlock your account.
2. depends how you created your account. If you chose "WALLET MODE", your password is to unlock your wallet that is stored in your browser. If you chose "ACCOUNT MODE", your browser doesn't store anything, but your password is used to regenerated your private keys.
It is important to keep the *PRIVATE KEY* as private as possible!! while the public key is derived from it in a one-way-only way and can be public.