I’ll work through your questions one at a time.
Q7. 1. Good spot! Contacts 11-14 are indeed a potential way for the pump to get neutral through the float switch. However, the float switch only closes when there is a flood condition in the dishwasher. Since a flood isn’t part of our current troubleshooting scenario, we don’t need to pay any mind to the float switch.
2. Since we know that A9 and A12 are electrically equivalent points, there’s no virtue to picking one over the other — they function exactly the same way for the purposes of this test.
Q8. The question specifically states that the inlet valve is not receiving line, so that’s where you have to proceed from with troubleshooting. If line is not present when it should be, then you have to be dealing with either a failed timer contact (which is ruled out) or a broken wire.
Q9. You’re correct, it would make more sense to start with the door switch. The scenarios set up in these questions are not necessarily supposed to show what an ideal troubleshooting process looks like. Rather, they’re supposed to set up a situation where you have to figure out what the best next step to take is.
Let me know if anything is still unclear!