The question instructions are saying that for any chiral compounds the professor drew in the possible answers, you are to assume that the product is in equal amount with its enantiomer - thus, the chiral compound is a racemic mixture.
Your answers are correct. However, your intermediate in problem 2 is not correct. There is no carbocation in the peroxide mechanism. Your intermediate for 3 is also incorrect. In the first step of the mechanism, one atom of bromine adds syn across a double bond. A wedge and a dash is incorrect. Additionally, the bromonium intermediate is charged.
(edited for clarity)