If I understand correctly, it's the pink rod in the pic below that is hanging loose, right? That is the
exterior latch rod #7, as you said, but it's easier to see where it goes in the right side version, where they have
interior latch rod also numbered as #7. They are both door handle rods, but not the same rods. The
exterior latch rod drops into a hole on an arm that operates the latch mechanism. You can see the hole from above with window down. If both of your latch rods are having issues, it is very possible that the latch itself needs replaced as without a proper spring tension, I can see how that arm would fall away from the exterior latch rod and leave it hanging. It also explains why your interior handle is also acting like you lost a spring, but the way it attaches it won't just fall out like the exterior one.
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