Is it because the designers of the course sentences were intending to teach us something about gender in grammar?
I mean, the second word in this sentences goes well with Bob's being male, and the 3rd & 4th words comply with eachother (that is, "brown" needs to be used in female form since "skirt" is female).
If so, the lesson is, the gender of the possession hasn't got anything to do with the gender of the owner, or vice versa.
Well yes. As far as I have figured it out, the gender of the adjective is based on the gender of the noun it describes. Skirt ( تَنّورة ) is a feminine noun so the adjectives describing it will become feminine i.e. بُنِّيّة. The دَك at the end of عِنْدَك is a hint that to whom (gender wise) this sentence is addressed is a male, which is confirmed by the addressing the person himself at the end with يا بوب.
Bob, Seth and George are sales assistants at a clothing store. Of course, Seth dreams od designing his own collection and so he will come in contact with Judy and Carrie, both rather affluent due to their high paying tenures as professors. Maybe we can see Seth explore his "feminine side" by befriending the local gay couple? Stay posted!