How to add (print) custom button: "Add to friends" into custom user-profile.tpl.php

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You can manually provide these links with two important pieces of information, the uid of the user you are 'friending' and the relationships type id.

The hardest part of this is finding the id of the user you are currently looking at and want to friend, you can provide this as a hidden field in a view, or do a lookup through php, but it really is dependent on where you are looking for the information from.

The relationship id can be found on user management->relationships->list and hovering over the edit button for the relationship will show you the id in the url.

You can then build out a link using the following format:
http://example.com/relationship/%userid/request/%relationshipid
So for user 8 and relationship 2 you'd have:
http://example.com/relationship/8/request/2

Setting to fixed, switch it back if you are still having problems.

How to hide this link if u're already friend with this user?

Have a look at #420714: "add to contacts" link and hide profile fields if not in relationship you could wrap your links in a similar if condition that uses user_relationships_load