What would be the most non-polar covalent bond possible?What would be the most ionic bond possible?

The most non-polar? A covalent bond is either non-polar or polar. If it's non-polar, it's not more non-polar than any other. H2, O2, N2, CO2, and CH4 (Methane) are all good examples of non-polar covalent bonds, and since they're all non-polar, they are all equally non-polar. The most ionic bond possible would be lithium flouride.

Wrong answer.

Yes, H2, O2, and N2 bonds are totally non-polar, but the CO bond in CO2 is polar, it is just cancelled out by the other CO bond in the molecule.  The CH bonds in CH4 are not very polar, but they do have some polarity.  Any diatomic molecule that has two atoms of the same element would be non-polar.

The most ionic simple bond possible would not be LiF, but rather CsF.  The polarity is due to the difference in electronegativity.  Fluorine has the highest electronegativity, and Cs the lowest (Note: Fr would have the lowest if any existed, but there are only ~20 g of Fr on Earth.)