Organizing and accessing contact information in Outlook.com
I have a Galaxy S7 Edge with Android 7. I spent hours looking through the many threads reporting the same issue where hotmail/outlook/live contacts are not showing up in your native contacts app. Here is what finally worked for me:
First, I have two devices. First, a Galaxy S7 Edge that is shattered but working. The contacts have always sync'd fine on that device. Second, a new replacement Galaxy S7 Edge that is fresh off a factory reset, but otherwise setup exactly the same with the same OS version, apps, etc.
So, to recap, the shattered device was syncing contacts, the new device was not. After deleting and re-adding my hotmail account several times and trying various settings on the new device, I finally gave up and decided to try exporting my contacts from my old device manually. Export/Import procedure: Contacts app -> Settings -> Import/Export contacts -> Export -> copy *.vcf file off the old device with USB cable -> copy *.vcf file on the new device with USB cable -> Contacts app -> Settings -> Import/Export contacts -> Import.
All my contacts were there, but I was concerned about syncing still. Just for fun, I added a new contact to my old phone that I new was still syncing correctly. Low and behold, it immediately showed up on my new device that, before manually importing the contacts, was not syncing. So, it appears somehow the import process kickstarted the syncing...
Hope it helps someone else.