My car is behaving funny. When on P or neutral you can hear it vibrating. Something that was not happening before. It is taking too long to for gears to shift. I think I fueled with adulterated fuel. What are the signs that a car is on bad fuel. How can I flush the system. Can I run the engine untold all the fuel is burnt out.

I wouldn't blame fuel as yet. Check your engine and gearbox mountings (vibrations) and ATF level (delays in gear shifting). When was the last time you changed or topped up the ATF?

Sounds something else rather than fuel.

From my experience after once fueling in a funny fuel stations, contaminated fuel results to low engine power, unusual smell from the exhaust and low kpl

Hakuna kingine, shida ni either or both of the above.