1. The fuel pump works when I connect it directly to the battery.Apart from what has already been discussed, check the ground block even though your 09 shouldn't be affected by the issues on the 07. Did you check if the pump works powering it directly from the battery? Check to see if the ECU is sending the signal (+ or -, can't remember which) to activate the pump relay. Are you also getting the same issues with the hand warmers? Do you have the updated red pump relay?
Could be a defective relay. What temperature are you trying to start it in? If it's below -15c, it could be the relay. A voltage drop could indicate a bad contact in the relay and it might not be able to handle an actual load. Try putting a headlight bulb on it and see if that voltage drops even more.2. I unplugged the plug from the fuel pump and checked voltage there when I turn the key on. I measure 12.5 volts. This is a little weird because the battery measures 13.1 volts. So I'm losing about 0.6 volts through the system. Not sure if that is a big deal.