When creating a Metamask wallet as a Chrome browser extension, what are all the different identifiers that match the wallet to its owner? Since it takes a password to log into the Metamask wallet, does this mean there is an e-mail associated with the account? Are there logs kept of the IP address where the Metamask was created? What are other identifying features are there?
To connect to Metamask and recover the wallet an user needs respectively a password and a seed :
- seed (also called mnemonic) : 12 secret words generated from the private key. You should never share these words, as they enable to access your funds. The seed is the only thing one need to recover his wallet.
- The password : it encrypts the account locally, that means it allows the user to access his account only from the browser where the Metamask extension is installed.
To summarize, when you create a Metamask account, you are given a seed derived from your private key. This seed is encrypted locally in your browser by the password you chose, used to unlock your account. To recover your wallet on another browser/computer you will need your seed that you will encrypt with a new password.
Regarding the IP address I understand Metamask knows it but does not share it with third parties (according to their privacy policies).
In a previous release, the user address was automatically shared with visited websites. As the websites know your Ip, they could possibly link your Ethereum address to your Ip (more info here : https://github.com/MetaMask/metamask-extension/issues/6325). Since the v7, a privacy mode is enabled by default and Metamask asks the user before sharing the address with the visited website (more info here : https://medium.com/metamask/privacy-mode-is-now-enabled-by-default-1c1c957f4d57).
Also, note that Ethereum is not anonymous but pseudonymous. Users are identified by their address and their activity can be tracked.