Please note that possessive adjectives agree with the object (a noun) in gender and number RATHER THAN THE SUBJECT.
In this exercise "la robe" is the object and is both feminine and singular, hence the choice of "sa" rather than "son" (for a masculine singular object) or "ses" (for a plural object of either gender).
Nope, there isn't really a his/her in the way you're used to, since in French the gender of the possessive word you use has to match the gender of the Thing Owned and not the Owner. So yes, this sentence can translate as both 'His only dress is black' AND 'Her only dress is black'. ('Robe' is a feminine word, so you use a feminine possessive word.)