How do I view my relationship to a living person I've been messaging on FamilySearch?
The Relationship Viewing feature works well if you find another contributor who has made a change or contribution to an individual in Family Tree. However, if it is someone who has messaged you and you don't have any of their contributed information in Family Tree to reference, you cannot see their relationship to you even if you have both enabled relationship viewing.
When you click on their name on the Messaging screen, there is currently no option to see your relationship or request that they make that available like you can on an ancestor's page. Your only options are to send a message, report abuse or mute them.
I can print "Temple Ready" cards for many individuals who I do not know. When I select "View Relationship" it will show me a tree of how I am related. How are these connections made and how do I know they are accurate.
You see a connection to that person because there is at least one path through Family Tree from you to them.
To examine the path or paths I like to use RelativeFinder.org.
To evaluate the accuracy of a path I first examine the historical records attached to each person along the path, with special attention to records that prove relationships. I also use the edit buttons on the Details page for each person to check birth and death dates and places. If there is a mix-up it will often be revealed in those details. Finally, I look at the Timeline Map on the Sources page for each person.