I had to jump through a few hoops to get them on the phone.
I found a link (can't find it now), which outlined the process. What worked for me is connecting the phone to the PC (Windows 7), and copying ringtone files to the phone's Ringtones folder. The key here for me was to copy m4a files not mp3 files - I originally copied the latter, and those weren't available in the list of ringtones to assign to various contacts. When I was copying an m4a file, I got a message whether I wanted to covert it, having said "yes", m4a file is converted to wma, and that format works. The bottom line is - you cannot use mp3 files as ringtones.
Yes you can! Although I've not tried with W10M only WP8.1. The trick is to transfer them using a PC to the Ringtones folder, if you download them from say OneDrive and move them using the Files app on the phone it doesn't seem to work.