There are no gears in the car as it's CVT. Get the ATF fluid drained ASAP, It's not designed for CVT, only use Toyota genuine CVT fluid.
Vibrations in Vitz is normal. Always mix high octane fuel in the tank to delay the ignition slightly and avoid knocking (3 cylinder).
You may be looking for gear changing but there isn't one. Vitz will never launch, this is hardest part of understanding vitz. It will never spin the tires even if you floor it as power transfer is linear. So keep a light foot on throttle.
Seriously, Get the ATF fluid changed ASAP, use CVT fluid only. I am not sure who in his right mind suggested you to use ATF fluid. You may be looking at 50K loss for replacement if something goes wrong.