Is it possible to use an spring underneath the piston of an engine so that it moves with high velocity than that of the movement of crank shaft after the suction and compression strokes and thus prpvide ore power and reduce the fuel consumption

I think you have answered your own question. A free floating piston can not provide "suction" on its own. That is why you have a crank style system even in rotary engines. With compression stroke the spring would help but with the vacuum portion there would be no kinetic energy to drive the piston down to create vacuum.

Is that the rotational motion of crank shaft that leads the piston of an engine to move upward after coming down?

Yes.
The explosion above the piston helps drive it down too.
A spring would need an opposite action to drive it down before it helps drive a piston up.
Having a series of pistons alternating on a crankshaft adds something, although mostly it smooths out the rattle.

Is that the rotational motion of crank shaft that leads the piston of an engine to move upward after coming down?

Yes, because a crank by its nature is offset. The offset is what provides the stroke of the motor.

Here ae some examples you can see.



https://www.youtube.com/watch?v=O9tfIfwlmz8


https://www.youtube.com/watch?v=zA_19bHxEYg