The switch from open to closed loop can be as little as 20 seconds after starting. It all depends on initial temps.
I don't know the ins and outs of LPG systems so not sure how LPG fuelling is controlled and how rich it can go.
With petrol, the PCM switches from open to closed loop when it thinks, based on an internal timer and initial temps that the O2 sensor has reached it's operating temperature. If the O2 sensor heating element is bad, the O2 sensor will not be within it's operating temperature range, but the PCM assumes it is and fuels the engine accordingly. The misfuelling that results causes running problems until the exhaust gases heat the sensor to it's operating range. At that point normal operation resumes and all is good till the next cold(ish) start.
Normal diagnosis of this is to just unplug the upstream O2 sensor and see what happens. If there are no running problems with the sensor disconnected the sensor should be replaced.
Normal heater resistance is somewhere around 5 Ohms.
Hard start could be fuel pump or filter/regulator. It could also be leaking fuel injector(s). If you can get a fuel pressure test kit that goes between the fuel line ane rail, and has flexi hoses each side, you can clamp off each side to test fuel injectors of pump in turn. Other ways to check for leaking injectors are removing plugs and looking for wet plugs or pulling the fuel rail and looking for drips from any of the injectors.
