Can an extremely small force lift a mountain in a hydraulic system? If not, then why not? 
As you see in the picture, a car can be lifted with a small force F1.
Here it is shown that 'F1 . A1 = F2 . A2'.
What will happen if A1 is of the size of a pin's cross-sectional area. Can a child lift a truck in such a way, using a safety pin? If not, and I feel not, then what is it that will prohibit this from happening? Will the metal structure break? Assume that the child does not hurts itself with the pin as it pushes it...
 A: 
What will happen if A1 is of the size of a pin's cross-sectional area. Can a child lift a truck in such a way, using a safety pin?

Assuming an incompressible fluid is used and that nothing structurally breaks, the answer is yes, a child can lift a truck.
This may seem unintuitive at first glance. However, if you've ever worked in a car shop, you know that a person can lift up an entire truck by pushing a small lever up and down on a car jack; this notion of force amplification by using different areas is the guiding principle behind how hydraulic jacks and related technology operates.
There is a trade-off, however. When you push down the pin a distance $d_1$, by conservation of fluid volume you will also have 
$$d_1A_1=d_2A_2\rightarrow d_2=d_1\frac{A_1}{A_2}.$$
For example, with a pin of diameter 1mm and a truck on a platform of diameter 2m, if the child pushes the pin down by 6 inches, the truck will lift $d_2=38\text{nm}$. This is so small that you couldn't even see the truck lift up. So in essence, you're trading more force for less lift distance.
You can also compute that this process obeys conservation of energy in a similar matter, using the forces and distances instead of forces and areas.
A: "Give me a place to stand and with a lever I will move the whole world"-Archimedes.
Yes, in principle the mountain could be lifted. However, the distance it would be lifted would be extremely small compare to the distance the pin moves.  The ratio of the distances moved is the same as the ratio of the cross-sectional areas.
