Ford Falcon 2013 Dedicated LPG, Engine Shaking at Low LPG
I bought a ford falcon 2013 from a dealer less than a week (122000 km). It was running good but one day the engine started shaking and the yellow engine sign on the dashboard appeared. This happened just after starting the car and it was happening while driving too. Even driving in this condition, the DSC warning light also appeared. I noticed that the lpg is only quarter tank left (as can seen in the fuel meter). So I filled the tank and the shaking, yellow engine sign, DSC light everything disappeared. For further information, before buying the car I took a test drive in the dealer showroom, and that time there was less than a quarter lpg in the tank. The dealer filled it up to three quarter. After that I did not fill the tank until this shaking thing happened.
Another issue I faced is the battery. I stopped in the coles parking and after shopping only for 15 minutes I returned back. But the car did not start after several tries. I called my friend and he came with a jump starter and the car started with it. I drove the car smoothly that day. But again I faced this battery issue today. To me, it seems like the car is taking a little longer than usual to get started. Which indicates insufficient charges in the battery. I also checked the battery by Supercheap auto, they reported that the battery is good but it needs charging.
Now, please tell me are these two issues are correlated? What may happen to the car?