Can I sync all my contacts and calendar items with Outlook.com and at the same time my iPhone?

Hi,

I am currently running Office 365 Home Premium and I have the Outlook part hooked up to my Gmail account. In order to get the Contacts and calendar items to sync with my iPhone (and Gmail), I have an add-on, which does not work with Office 365.

So here is what I was hoping to do.

Ditch Gmail, and move my domain from Google to Outlook.com with the hope that all my emails, calendar items, Contacts and tasks also will be synced not only with my Outlook in my Office 365 installment, but also with my iPhone and iPad, so that if I delete an email or a Contact on my iPhone, this would be reflected on Outlook.com as well as in my Outlook on my PC. And if I create a task on my PC in Outlook, that task will appear on Outlook.com and on my iPhone.

So firstly, I need to find out if it will turn out as above, and if so (or with some minor limitations that tasks does not sync to iPhone), I will have to find a bullet proof way of migrating my domain with all my emails from Gmail (I am using IMAP), to Outlook.com, making sure that all other email accounts within my domain can get clear instructions how to do the switch without loosing emails and Contacts, etc!!!

So if there is anyone out there who could clarify some of the above, I would be most grateful!!

Thanks!