All the emails are not showing up because the email clients on phone generally pick up emails from a specific past period only. You can say from last 2 weeks or a month only. you have to choose the option of syncing the emails that are older than that period, or you can say from the beginning of your mailbox. This consumes a lot of data and before choosing this option, you should also change the auto download of attachment to manual, which will make the process quick and easy.
Why don’t all my emails show in my Yahoo account on the Nokia Lumia 625?