You can set up mail forwarding in Yahoo, if you use the web-based email. If, instead, you use POP or IMAP for Yahoo, then yes, you can use it with Mail.
Also, I don't understand "Mozilla email." What is that? Is there some email service that Mozilla provides, or are you referring to Mozilla's email client?
Mail doesn't support certain email providers -- it supports different ways of connecting to email servers. It supports a number of different connections, including POP3, IMAP, .Mac and Exchange. If your email service is based upon one of those protocols, then you can get the email with Apple's Mail.