I don't have problems in using Yahoo Mail with Firefox.
As for having your Yahoo Mail forwarded to a different address, if you have the basic e-mail (not the paid version Plus), you are not allowed to have it forwarded.
Now, as for GMail, you ARE allowed to forward the messages. What you COULD do is create a new GMail account, have it forwarded to your Yahoo Mail acoount in the beginning, and in Yahoo Mail change the Reply-to email address (see the Mail Options->General Preferences), and make sure you mention to the people you are sending messages to of your new email address. Just a thought.
malu