What you are seeing under the opamp is a via, not a test point. We don't need to probe that. We also don't need to worry that you don't read continuity to whatever else you were probing, since the via is tented and you're actually just testing continuity to the solder mask. We can leave this one alone.
While this is getting a little outside my comfort zone, I believe that the negative ohms readings are resulting from taking measurements within the active circuitry while power is on. True or false? If that's the case, can you remove the unit from power, make sure the caps have all discharged and you no longer have voltage sitting on any components, then redo the ohms measurements? I should have been more specific.
Although it's quite difficult to tell anything from a cell phone photo (this is not just your photos, but everyone's), it does look like we may have a few candidates for cold solder joints in there, as well as several that have been clipped deep into the joint itself.
I'll also try and pull my prototype unit out of the rack tomorrow to take a few measurements to compare to the new ones you will take.