Electronegativity increases up a group because the bonding pair of electrons is held increasingly further away from the nucleus as the number of shells increases.
Non-polar bonds occur if the two bonding atoms are identical, as their attraction for the shared pair of electrons is equal and the electrons are equally distributed between the bonding atoms.
In magnesium iodide, a small difference in electronegativity between the magnesium and the iodine results in polarization of the bond, with the electrons shared unequally and resulting in an uneven distribution of charge.
In nonpolar molecules, the symmetry of the molecule means the effect of any permanent dipoles is cancelled out and there is no difference in charge across the molecule.
The lateral density relates the probability of finding electrons at a particular position in space, represented as a cloud of electrons around the nucleus.
Molecules containing polar bonds are not always polar, but the symmetry of polar bonds within the molecule can cancel out the effect of any permanent dipole.
When drawing Lewis structures, the bonded electrons are represented as a line between two atoms, visualized as being shared equally between those two atoms.