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the coax and ant should show 40 to 50 ohms depending on a few things, but should be closer to 50
You are confusing impedance with resistance. An ohm meter is useless unless you want to measure continuity. You would need an impedance bridge to measure what you describe.

Also, there is no answer to the q what the typical resistance should be between the shield and inner conductor of the coax - it depends on the feed system to the antenna which can appear as a short with an ohm meter.

If you really want to determine what is happening at the antenna, you either need to remove and inspect everything or use an impedance bridge and SWR meter,
 
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