Without an app you cannot sync yahoo contacts. It will sync your Gmail contacts and email by default. If it is not syncing your mail I would check your settings. Something either isnt set right you there is a problem with your phone.
Go into accounts and sync. Then under google make sure contacts syns in checked. Try to go a manual contact sync and see what is ways.
You can add Yahoo mail via an app. If you wanted to sync your yahoo contacts to your phone too theres an app for that.