In view to keep my fig tree growing fast or having more fruits etc. does it help if I cut off certain lower parts leaves ? Any advantage or disadvantage of doing this ?

Leaves do give and take i.e. consume some nutrients and moisture but provides back through photosynthesis.
Depending on your plant size, if the leaves are shaded then removing them may not be detrimental to the plant growth. 
Some people remove some leaves during the ripening period too provide more sun shining on the fruits. 

Thank you for your respond. I am thinking to remove some leaves near the bottom to create better air circulation for the trunk. Besides it might be better to give more nutrients for the new branches or fruits. Please correct me f I am wrong. Thanks................

I was advised to cut away the inner branches to let in light, heat and air.
It definitely helped! I took out unproductive growth and pinched back everything
else to keep the tree under 7'. I like bushy trees with reachable fruit.