The series EE interest rate is 4.04%. The savings bond web site says that you buy it half the face value. I do not know much about EE. Do they calculate the interest on what I pay for it or on the face value?

The face value on the bond is essentially meaningless, except that the government promises to pay you that amount after 17 years. That is, if after 17 years the value of the bond hasn't caught up to the face value, you are guaranteed to get that face value anyways.