Does SRS/air bags measure Ohms/resistance for operational command?

Yes, the airbag system measures resistance values in the circuits. You definitely should repair the damaged wiring and inspect the weight sensor in the passenger's seat. A word of caution here, do NOT use a self powered ohmmeter to check the resistance values in the circuits! Doing this will deploy the airbags!! For this type of repair you really need a factory shop manual for the vehicle to properly check the system. Another thing to be aware of is you're not seeing random flashes from the airbag warning light or hearing random beeps. You need to count the flashes of the airbag light or count the beeps you are hearing. If you're hearing 5 beeps and a pause then 5 more beeps that's trouble code 55. The airbag computer also will not store trouble codes. Many years ago I had a 94 Escort. Long story short I took it to the Ford Dealer for a flashing airbag light, code 44. They said it was the clock spring. High resistance value in the circuit. So I replaced the clock spring and it didn't fix it. The car was totalled in a front end collision. The night of the accident the airbag light was not on, it had been an intermittent problem, so the system should have been active. But the airbags didn't deploy. Unfortunately the moral of the story is you might be chasing down a problem that can't be fixed. Good luck to you I hope you can fix it!! Jim