Well that's a pickle... I have no memory of there being 4 pins instead of 2. I suppose if I found myself in your situation right now, I would unplug the other sensors and look for which specific combination of pins (on a working sensor) gives me 10k Ohm. Then just bridge those two pins on the connector for the faulty one.

To answer your question more directly: 1) you only do one bridge (one resistor). 2) Per above, I don't remember. However, in that second photo it does look like it's Pin 1 and Pin 2. The placement of the resistor is just to accommodate routing for the connector to go back. There's no fancy business happening off screen in those folds. I don't think I put my connector back together like that... I think there's multiple ways for the resistor to fit. But it really is just a simple bridge of the two pins. My only question is that it doesn't look like the lead actually hits Pin 1 in that photo. Maybe it's just optics. That's the only reason I think you're safer to test a good sensor to make sure it's the right pins.