What is causing my 4 cylinder 318i BMW to vibrate or tremble when I put it in drive or reverse. Once it is in park it seems to be fine or if I turn on the AC it trembling minimize also when I accelera

Ignition firing order is 1-3-4-2.

Ignition firing order is 1-3-4-2.

This light is telling the brake master cylinder is low on fluid

The first thing to do is put the front tires on the back and see if there is a difference.It could be a bad tire,or a balance problem.There could be worn front end parts and that will show up as movement in the wheel by moving the tires back and forth.worn tie rods or ball joints can cause a vibration.If the vibration is when the brakes are applied,then the cause is most likely a warped rotor.Check the temperature of the front rims and if one is much hotter than the other there could be a sticking caliper,which will cause the rotor to heat up and cause a vibration.

possible air mass meter fault or split concertina air hose between airr flow meter and manifold

you have problem with tank mybe is dirty and you must check fuel filter and fuel pump

while driving at higher speeds you may not notice a sound as much as when you are drivng in reverse as you usually drive slower in reverse. This leads me to think that the rattling can be caused by a loose protective plate under the car. When a load is put on the engine, it tends to vibrate more this vibration can cause a lose plate to rattle more. This is the cheap answer. That is if you are definitely sure the sound is coming from under the vehicle. Otherwise, you may have a crank shaft problem or a seal in the bottom half of the motor could be bad. You may want to crawl under the car and try to shake some of those plates underneath. If none of them are loose take the car to BMW it shouldn't cast anything for them to look at it unless they have to hook it up to the computer.
Please remember that if you intend to climb crawl under your car, you must make sure that your car is properly supported to prevent serious injury. Also, if your driving with a loose plate, it could easily fly off while driving or if you hit a bump. This could cause serious damage to your vehicle. Also, please check you oil levels and make sure you do not have an oil pressure light coming on when you hear this noise.

bad engine mount make car shake.cylinder misfire make engine shake.

when it does this ,see if black smoke coming from tailpipe...could be your oxy sensor not reading fuel ratio ...age seems about right for bad sensor...also if you change this ,take car for a good driveapp.20 mi. to let new sensor get a good reading on fuel /air mix coming from engine exhaust

simply open the boot & remove the blown bulb & replace with a new one. the bulb is just a half turn holding in there so turn it anticlockwise & it should pop out.