Not sure on a Windows phone but with my Android phone I don't sync e-mails direct with Outlook. I set up e-mail accounts on the phone as if it were Outlook. With POP accounts it is important that e-mails are left on the server otherwise each device cannot see them and with pop accounts sent e-mails are unlikely to be visible. It is much better to use an imap e-mail account as then you get sync on any pc, smartphone, ipad, etc.
Best Android apps 2015/2016: Best apps for your new phone or tablet - what apps should I download?