Do interest rates fall when the money supply rises, because there is excess reserve and the banks have to loan it out to someone to make a...

We can thing of interest as cost  of borrowing money. and Money supply as the money that is available for spending directly or through borrowing. Thus when money supply increases, the money available with banks for lending increases, and in line with the law of demand and supply, the banks need to lower the interest rate to lend the additional money available with them for lending.

Also, the banks also try to reduce the interest paid by them on the money deposited in the banks by people when they have more money than the they need for borrowing at the original interest rates. Thus interest rates paid by the bank as well as that charged by the bank tend to fall when the money supply increases.