I mean, Is it possible to use the fingerpicking classical musicians use in their classical guitars on the acoustic guitar? Do we have to use the same position? 
Do we have to grow long nail or use finger picks? 

Well first off, steel strings will chew your fingernails to shreds.

Second classical bodies are approximately the same size as an "orchestra" model steel string.

Placing the guitar on the left leg, give more freedom of movement to your fretting arm, shoulder and wrist. However, it does feel quite alien if you've played with your guitar on the right leg for any length of time.

Nylon string guitars generally have very wide necks, usually on the order of 2", or 53mm.

All that having been said, yes you can plat a steel string in the classical style, but you need to be almost 2 times stronger to do it, because of the much higher string tension of the steelies.