Why do the boiling and melting points decrease as you go down group 1 and vice versa for group 7?
The group 1 elements are the so-called alkali-metals. The bonding between the atoms is caused by the interaction of the nuclei with the delocalized electrons. With increasing number of electrons and protons, the atomic radii get bigger and hence this interaction becomes weaker as the average distance between nuclei and electrons increases as you go down in group 1.
The group 7 elements are the so-called halogens. They exist under normal circumstances in their molecular form ($\ce{F2}$, $\ce{Cl2}$ and so on). In contrast to the group 1 elements, the dominant intramolecular force here is London dispersion (or van der Waals forces if you prefer). This attraction is caused by the correlated motion of electrons. With increasing amount of electrons, there can be more correlated motion and hence there is a stronger interaction between the molecules and an increasing melting / boiling point when you go down in group 7.