im not sure where you are getting 13 in the dollar.
where is it? front? back? left corner? right corner? middle?
there are numbers on the dollar...
its not a phoenix.
its an eagle.
ADDED--
the only 13 that represents anything pertaining...is the number of stripes on the american flag and they represent the original 13 american colonies.
i don't believe the 9 feathers have a significant reference.
oh. do you mean the 13 stars above the head of the eagle?
they represent the original colonies as well.
i found a link that explains many of the symbols and why they were chosen.