I have few questions regarding my car:
 

1)It’s about cold start- When starting the car, the engine shake slightly and there’s some petrol smell which I assume it’s normal. The smell is gone after like one-two minutes and the shaking like after 2-5 seconds. But my question is, when the car is in idle for like 15 minutes, I still can smell some sort of “Fuel like” smell from the exhaust? What type of smell usually comes out from the exhaust?

I'm just wondering what if the any car engine does have some petrol/fuel smell druing cold start.Is that normal?

2)About my tyres- I’m not sure if it’s normal or not but it seems flat. I brought it to the tyre and pump more air in but it’s still looks flat. I’m not sure why. Here’s a picture.
http://files.unitedbimmer.com/ub.c/zeaq328i/Tyre.JPG

Re# 1- read Dudesky's DIY in the E36 knowledge base on the ICV (idle control valve cleaning) Excellant DIY! Sounds like your prob.
Re: #2 - It does l@@k low but get yourself a tire guage and check your air pressures and inflate them to the pressures recommended (on sticker inside drivers door post) Check them COLD not after driving.

32 psi for tires is normal.

the ICV could be it, also check your fuel line by where it starts to feed into ur fuel injectors(font of the car). Mine was a bit loose but i got a new braket and secured it to the fuel rail. check to see if ur not leaking any gas

What kind of oil do you use? Having the right oil might help on cold starts, I know when I switched from Mobile 1 5W-30 to Mobile 1 0W-40 the car felt a LOT better on cold starts :dunno. But do check your ICV vavles though, specially due to the smell.

And the pressure does seem a bit low on the tires

as stated about 32psi on tires is about avg. just get a standard tire guage and check it out.

I've not expereienced a fuel smell related to a dirty ICV, but I guess it could happen. I would be more suspect of the fuel pressure regulator maybe?