Q. Is it alright to download a picture of myself that was taken by a friend and posted on their Facebook page?

Unless the copyright ownership is transferred, your friend owns the copyright of the picture. 

By posting a picture on Facebook, the user gives Facebook a “non-exclusive, transferable, sub-licensable, royalty-free, worldwide license” to display the pictures over the internet. 

If you think that making a copy of the picture is unauthorized by your friend, then you shouldn’t copy it.

To learn more, visit https://www.facebook.com/legal/terms