what depth is required for a footing on which a pier will be placed to raise a girter or beam?

Answer 1

you will have to check the local codes. No one can answer this question without knowing where you live and knowing City and state code

Answer 2

Any pier must be deeper than the frost line, the depth that your earth freezes in the winter. In Minnesota that is over 6' deep, in southern California only 1'. Check with your building department, they will have that info.