Which of the following statements is true about the trend down group 7?
The answer is D, the melting points increase. This is absolutely true (source for values):
\begin{array}{lrr}
\text{Halogen} &amp; \text{Melting point}/^\circ\mathrm{C}&amp; \text{Boiling point}/^\circ\mathrm{C}\\\hline
\text{fluorine}   &amp; -220  &amp; -188  \\
\text{chlorine}  &amp; -101  &amp; -35   \\
\text{bromine}  &amp; -7.2  &amp; 58.8  \\
\text{iodine}   &amp; 114   &amp; 184   \\
\text{astatine}  &amp; 302   &amp; 337   \\\hline
\end{array}

And the boiling point increases, too, so answer C is definitely wrong.

Another obviously wrong answer is B, the atoms get smaller. With increasing main quantum number the atoms obviously have to become bigger since the main electron density moves further away from the nucleus. In numbers:
\begin{array}{lrr}
\text{Halogen} &amp; \text{Covalent radius}/\mathrm{pm}&amp; \text{Ionic radius }\ce{(X^{-})}/\mathrm{pm}\\\hline
\text{fluorine} &amp;  71  &amp; 133  \\
\text{chlorine}   &amp;  99  &amp; 181  \\
\text{bromine}  &amp; 114  &amp; 196  \\
\text{iodine}   &amp; 133  &amp; 220  \\
\text{astatine}  &amp; 150  &amp;      \\\hline
\end{array}

For answers A and E it cannot be unambiguously answered, because reactivity is not a well defined concept, see "What is reactivity really, and can it be quantified?"  for example. The IUPAC goldbook states, that reactivity is a kinetic property. It goes on to describe, that it can only be absolutely used in a given context or in reference to another system. However, it is also often used in expressing general trends, which is the case when looking at this question.
Given this context, you can find the following portion on UC Davis ChemWiki:


  Reactivity of Elements: decreases down the group
  The reactivities of the halogens decrease down the group ( At &lt; I &lt; Br &lt; Cl &lt; F). This is due to the fact that atomic radius increases in size with an increase of electronic energy levels. This lessens the attraction for valence electrons of other atoms, decreasing reactivity. This decrease also occurs because electronegativity decreases down a group; therefore, there is less electron "pulling." In addition, there is a decrease in oxidizing ability down the group.


In this context, answer A is wrong. However, I would not consider E to be strictly true either. Have a look at the electron affinities, and you will find, that fluorine behaves anomalous. This was also discussed in "Why does chlorine have a higher electron affinity than fluorine?" 
However the general statement will usually be given as: "Electron affinity decreases down the group."
\begin{array}{lc}
\text{Halogen} &amp; \text{Electron Affinity}/\mathrm{kJ\cdot mol^{-1}}\\\hline
\text{fluorine}  &amp;  -328.0  \\
\text{chlorine} &amp;  -349.0  \\
\text{bromine}   &amp;  -324.6  \\
\text{iodine}    &amp;  -295.2  \\
\text{astatine}  &amp;  -270.1  \\\hline
\end{array}
The same trend can be observed with bond enthalpies of the $\ce{X2}$ series (source):

This trend is broken for the hydrogen halides $\ce{HX {(g)}}$.



Your assumption is therefore correct, maybe you have already done the same analysis. However, we can only definitely state and proof, that answer D must be correct, while answer E might be correct depending on the reference system.