Is I2 Polar or Nonpolar?

Answer: I2 (iodine) is a nonpolar molecule because of its linear structure and the identical electronegativity of both molecules.

Due to the large number of electrons present in the molecule, temporary forces known as London Dispersion Forces (due to the distribution of electrons within the molecule) exist and enable the molecule to take a solid form at standard temperature and pressure. In fact, these temporary dipoles are so strong that this molecule has a higher melting point and boiling point than water at 114˚C and 184˚C respectively. Due to its status as a halogen with a large number of electrons, I2 has the capability of undergoing many different kinds of chemical reactions. 

This is similar to the reason why H2 is a nonpolar molecule. Read more concerning H2 specifically in this article about whether H2 is polar or nonpolar. 

I2 Ball and Stick Model. Created with MolView.

What is the importance of I2 (iodine) in biological systems?

I2 is very important in the creation of thyroid hormones. An iodine deficiency often results in cognitive disabilities and other negative effects. This is why iodized salt is commonly sold around the world to ensure that no one's diet iodine-deficient.