Can someone explain my professor's answers for these alkene additions?
In example A, you are right that the cyclohexane ring is more stable than the cycloheptane ring. There are two choices for rearrangement in this case: 

1) Ring expansion to form the cycloheptane ring 

2) 1,2-hydride shift to yield the tertiary alkyl bromide

The second product will be more stable and thus be the major product

In example B, you are right, a ring expansion is possible, so there should be the ring expansion product too. You will have a mixture of products in this case (1,2-alkyl shift, ring expansion, and no carbocation rearrangement)

In examples C, E and F, it is possible for the H-A to add across the double bond either way, so again, a mixture of products would be obtained

A lot of times, only one product is shown for addition reactions such as hydrohalogenation; however, it is important to remember that there are often multiple products possible.

Chemists very rarely utilize reactions that involve a carbocation rearrangement because a mixture of products is obtained, which results in very poor yields