I've decided to write this in case someone will really needed cause I had to spent lots of time before my Yahoo mail account was synchronized with a Windows Phone 8.
What is the problem?
When add yahoo mail account to all accounts to synchronize with windows phone 8 -> no connection is made and no mail are synched with you phone.
When you set up account sync with Phone using Yahoo option -> it uses POP3 methode to get mail by default and you cannot change this in settings. So every time you're trying to connet to mail using POP3 it does not connects. POP3 protocol is included ONLY on premium account YAHOO. That's why it's not synched (in case if you do not have premium account already)...