Translation:She is your wife.
Really?! How long was I asleep?!
Echtgenote is also a partner
Yes, but not all partners are echtgenotes. An ''echtgenoot'' or ''echtgenote'' is someone who is married, while partners may or may not be married.
edit: it just occurred to me that the literal translation of "echtgenote/echtgenoot'' is ''spouse''.
Which one is more common? Echtegenote or vrouw?
I would say that 'Zij is jouw vrouw' is more commonly used than 'zij is jouw echtgenote'. The latter is more formal.
Couldn't another term be "Zij is jouw vrouw"?
yes, if Duolingo doesn't allow it you should report it
Why can't we use "uw" instead of "jouw" here, if on a prior exercise of this unit they were interchangeable?
Probably it's just a missing translation, since "zij is uw echtgenote" is correct as well.
You should report it, so it can be added.