I'm not sure what you'd use the email for in the above scheme, but sure, that can be done. To transform a password into a key you'd need a password-based key derivation scheme (PBKDF). You could use the email as additional input, e.g. by using it as a salt or part of a salt.
Furthermore, you would need a mode of operation for AES. AES is a block cipher so itself simply takes a 16 byte plaintext as input and then produces a 16 byte ciphertext. A mode of operation can be used to encrypt multiple, longer messages. The result will however be at least as large as the password store: AES does not compress data in any way, and usually you'd need to store an IV and possibly an authentication tag.
Yes, you can store ciphertext in a public location. Storing it on a blockchain seems wasteful though. Generally, it seems more logical to store it in the cloud and keep local copies (and KeePass apps generally support Google and Dropbox, for instance).