To change your default "From" address, go to: Settings -> Signatures & Compose -> Compose options and it's the very first setting at the top. (Direct link: https://app.fastmail.com/settings/sending/composing).

You always use your username for authentication. (But it's not special other than that; you can send from any of your addresses equally.) You can rename your user to your address at the custom domain in Settings -> Team & Sharing -> User management. (Direct link: https://app.fastmail.com/settings/team/users).