If coolant/antifreeze is empty, will it cause to give p1580 error code

Yes, the coolant was low. I added it but still, it is giving p1580 error code and once the vehicle is started it is displaying ASR occ.skid on the display and the vehicle is vibrating a lot and also it gave smoky smell on the exhaust (last time I put little low quality fuel).

Ok get the throttle/accelerator motor checked out, that should eliminate your problem.