A username is yours to keep - only the owner of the game can change one, and you would be told by email if that ever happened.
Drawn for your username, so there is nothing to choose - and nothing to lose. It follows the account rather than the factory.
This is where a forgotten password is sent, so it is worth keeping right. A new address is not moved onto the account until you have typed back the code sent to it - so a slip of the finger cannot take the way home with it.
Changing it signs out every other device.
Scraps everything in the factory. The saved game is untouched until you press Save.
Every message this game has sent to your address, newest first. Press one to read it. A code or a new password is blanked out - it is taken out of the text before the message is written down, so there is no version of it here for anybody to read.
An account is only for keeping your factory in the database.
Nothing is written to the database until you press Save, so the game you last saved is untouched until then.