Why the solubility of the halogens decreases down the group?

Answer 1

The outer most valence electrons are the ones responsible for the chemical's behavior.
Each electron pairs up with a proton in the nucleus.
The greater the distance, and layers of shells that get in the way, dimish the forces on the electrons in the outer most shell.
For example, Flourine is the most electronegative element. It has 7 electrons, and will steal one more from any atom or molecule to get 8 ( full shell, Octet rule, nobel gas configuration).
Electropositive elements such as the left side of the chart, have a full shell, plus a few electrons, but no where near 8. They will provide energy just to loose one or two to revert back to a full shell. Lithium, Sodium Potassium etc. The larger the atom, the further the outer most electrons are from the nucleous, the less the pull from the protons in the nucleous. So the lone outer electron in Potassium is much more likely to wander off, than the outer electron in Lithium, making Potassium, more electro positive.
So what does that have to do with solubiity.

Well, more electronegative elements make stronger Ionic bonds. The electrons are held tightly by the chloride ion because it is electronegative, and holds the stolen electrons tightly. Larger atoms, dont feel the power of the electrical field as strongly, and bonds are weaker.
low molecular weight Salts that dissolve easier in water are more polar.

Answer 2

The intermolecular forces increase as you go down the periods. Because the solubility depends on how easy it is for the element to pull away from itself; the more intermolecular force there is, the less soluble it'll be.

Answer 3

Because of the increased atomic mass and increased lattice energy in the crystals.