Change signature based on send from email

This one's a little odd to wrap you head around, but I'll try.

In Mail.app, signatures are tied to accounts. Right now, as far as Mail is concerned, you have one account, therefore all three signatures are applied to it. The fact that the account has additioal aliases that let to use different email addresses is irrelevant.

The solution, then, is to create three accounts, not one account with three aliases.

Each accunt should have the same SMTP server settings.

In this way each account can have its own signature and the interface for selecting an account (and therefore, signature) for new messages is the same. You'll probably want to turn off email retrieval for the additional accounts, though, to prevent new incoming messages getting downloaded multiple times.

That doesn't work

It does work - you're doing it wrong 🙂

The ancilliary accounts should not be enabled. For what difference it makes you can set them to POP, or even set some dummy POP/IMAP server address - this account will never, ever be used to retrieve mail so it really doesn't matter what it's set to.

The SMTP server can be the same as your existing account.

This is only being used so that Mail.app offers another email address to send new messages from.

I can't help with the duplicate folders issue, but if you set the accounts to POP then there are no additional folders and you can also collapse the Inbox to hide the additional accounts.