These instructions apply only to EAS accounts in Outlook 2013 and 2016. If your Outlook.com account was moved to the new server (all older accounts should be moved by mid-2017), you'll be able to import CSV's directly in Outlook or upload appointments and contacts in other folders using drag and drop IF you remove the account from Outlook and add it back using auto account setup, which will add it as an Exchange Account.
As people start using Outlook 2013, I'm seeing more complaints that import doesn't work.
"When I try it import a CSV, it says "operation cannot be completed because the service provider does not support it" any ideas on why this is? What I can do to get around it?"
This error is the result of trying to import into an Exchange ActiveSync (EAS) account. The EAS service provider (Outlook.com / Hotmail) does not support importing CSV (or pst files) into the Outlook.com/Hotmail folders.
You can move Calendar and Contacts from a local data file into the Outlook.com/Hotmail folders.
Initially you needed to Copy calendar and contacts from a local pst to the Outlook.com data file, but a recent update changed the behavior and Move works now. If Move fails, try Copy.
Use IMAP to move or import Email messages into the Outlook.com account.
If you need to import calendar or contacts from a CSV file, you'll need to import them into a local .pst file then move or copy the appointments or contacts into the EAS account's calendar or contacts folders. If they are in a .pst file already, open it using File, Open, Outlook Data File and copy the calendar and contacts to the Outlook.com folders.
You can also use the Move > Copy to Folder command to copy the selected items to the Outlook.com folder.
If the items you copied are not synced up to the server after a few minutes, press F9 or the Send and Receive button.
Import Email into Outlook.com
If you want to upload email to Outlook.com, you'll need to configure the Outlook.com account as an IMAP account and move the mail into it. Once it has finished syncing, you can remove the IMAP account. You can have both the IMAP and EAs account in your profile.
This video tutorial shows how to add a new .pst to your profile and import the contacts (or appointments) into the .pst then move them to the Outlook.com account.