You would use the ohmmeter to check for opens or shorts in the coax when it is not connected at either end. Don't make resistance measurements with the ohmmeter with any voltage on the coax; you will zap the meter.
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So I'm looking at a resistance equal or near that to the rating, which I assume is 75Ω.
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No, that is the impedance of the coax for RF signals. The ohmmeter measures DC resistance, which would only be a few ohms for continuity of the center conductor from one end to the other. It would also be a few ohms for continuity of the shield from one end to the other.
If you don't have access to both ends near the meter when checking for continuity, short the far end and check between the center conductor and the shield and the end by the meter. It should be a few ohms. The test current makes a round trip out the center conductor, through the short at the far end, and then back to the meter on the shield.
To check for shorts in the coax, neither end should be connected. Make a resistance check between the center conductor and the shield at either end. It should be an open circuit, with no continuity.
Do the resistance measurements first. If the coax is OK, then do the voltage measurements.
When you make voltage measurements, start at the power inserter without the coax to the preamp connected. Measure the voltage at the connector that goes to the preamp between the center and the shield threads being careful not to short the voltage. I usually stick a short length of 18 gauge solid copper wire in the connector for the voltmeter probe.
Then connect to coax to the power inserter and check the voltage at the end of the coax that connects to the preamp. Again, be careful not to short the shield to the center conductor. I usually insert an F-81 adapter on the end of the coax and then insert a short length of 18 gauge solid copper wire as with the power iinserter.