Without further context, you are both right. Both alternatives are possible in each case.
Both "das" and "dieses" would be possible in a conversation. If you had two dresses to choose from, you could point to one and say either "Das Kleid ist schön." or "Dieses Kleid ist schön". Perhaps "dieses" is better in terms of style. (Please note that "Kleid" is always capitalized.)
There is nothing in the question to indicate the relationship between the two people. Correspondingly, one would say "trink" to a friend, or a doctor would say "trinken Sie" to a patient.
I'm pretty sure this is the test your question is about. In the test, these are questions No. 31 and No. 33.
31 - Welches Kleid gefällt dir? _____ Kleid ist sehr schön.
The given solution in the appendix also included is c = "Dieses". But as I said above, one can discuss whether or not also "b) Das" is correct. However, "das" is a bit more colloquial (and implies an elliptic "da"), so "dieses" may be the better alternative here. But the question "Welches Kleid gefällt dir?" could be answered by "Das da.". So we're in a kind of gray area here.
33 - Ich habe Halsschmerzen! _____ eine Milch mit Honig. Das hilft!
d) Trinkst du
The option (Trinken Sie) is not part of the answer options here. Maybe it was a different test, the teacher made a mistake, or you remember wrong. But in this case the only correct answer is also c = "Trink". If another possible answer were "e) Trinken Sie", the question could not be answered unambiguously because, as I said, both (c + e) would be possible.