You're talking to two people (second person plural) who have one thing ("Beziehung" feminine singular nominative) so you use the second person plural possessive pronoun "euer" and the feminine singular nominative ending "-e".
Just to make it more complicated, it looks like when "euer" takes an ending it becomes "eur" so you make it "eure".
You can remember the endings for possessive pronouns because they're the same as the endings you use with "ein". (It gets more complicated than that later but for now that trick will work.)
Fair has multiple meanings in English. The 'fair' that is used in that context is the 'fair' used to describe a beautiful person, eg: 'the fair maiden', this use of 'fair' is to describe ones beauty and originates from the era where it was desirable to have fair skin. You wouldn't use 'fair' in this context with that same meaning.
Schön can mean different (albeit similar) things in different sentences. "The relationship is fair" (when using a translation of schön) would imply that is isn't bad but isn't all that great either. Here, 'schön' implies that is a nice or even beautiful (the word I used that was accepted), so 'fair' just wouldn't fit.
in dictionary says that EURE is (f) Fluss , river and not pronoum YOURS correctt is EUER