Close... real close...
> Vector means maybe in this case energy changing direction?
Vector as in directional force vectors. Energy is too vague. And I think is a different formula in physics terms.
> Pushing against an arm? = as in pushing hands maybe?
> Neutralise an incoming force (push)
This is where sensitivity (listening jin) is important.
> By redirecting (thus the term vector) it into the ground(Earth)
Now how to bounce it back...?
> Done by the correct body alignment( as explained by Bossman?) and relaxation of the body( the person who is being pushed)
These go hand-in-hand...
> so there is no firm resistance against the force(push) on its way to the floor(Earth?)
Tension... not resistance... when you tense your shoulders (to resist), you get pushed over. If you are too floppy, you collapse and then get pushed over. Tension is somewhere in between loose and tensed. (See previous point re: body alignment and being "relaxed").
> The legs acts as springs( thus the use of one legged squats and other resistance exercises done by IMA's and others)
Leg strength is important, very important. Get off the computer and sit in mabu.
> The term root is said to be the contact between the person and the ground.(Earth)
Yes, you need a good root...
> Personaly I guess it has to do with the amount of strength and correct use of the legs/body muscles as to the amount of power obtained??
It depends on WHERE the power is sourced from that makes it "internal" or "external". Large muscle groups is external... true internal is sourced from the feet and dantien. And then you have varying degrees of everything in between.