[Yahya A.Sharif (OP)]

space time is curved everywhere due to the mass of the rest of the universe. So you can never say that the effects of gravity are zero.

So in reality you can't reach  an infinite space nor a zero effect .There is a misconception here infinity is not a real number so it is not possible to say if you travel infinity distance gravity effect is zero also according to the gravitational equation you can't substitute infinite distance, even though in reality you can't reach infinity  it could be a thought experiment that is if gravity effects decreases continuously we have a limit for that decrement which is zero effect then gravity effect in fact has a limit but space doesn't so what happens at that limit when gravity force equals zero space would still be increasing.
second the universe started at a moment in the past and all masses existed at a moment. infinity doesn't have a limit it is continuous if mass bend continuous space you can't start an event "mass existence" and have its effect at infinite distance"no limits" space can't be bent infinitely because infinity is unreachable mass can't bend a point in space at infinite distance since this point can't be reached.

[Bored chemist]

I was able to easily falsify the existing fact.

That's logically impossible.

[CPT ArkAngel]

In principle, gravity has an infinite reach. In reality, gravity reach is limited by the speed of light. The universe is probably finite and the global solution is also probably finite and quantized. The most important thing about a physics theory is that it is based on real assumptions or at least on better approximations than prior assumptions.

[Yahya A.Sharif (OP)]

In principle, gravity has an infinite reach.
The universe is probably finite

Space is a container for every universe that might exist so it's infinite , if the universe is finite then gravity is finite .Finite universe results in finite gravity.

[Yahya A.Sharif (OP)]

How mass curves space? What is the mechanism?

Just to add this.
The existence of mass causes non-existences in space causes the space to displace and bend .Mass started bending space at a moment"mass existence " and it continues bending it and spread out with the speed of light c.

[Yahya A.Sharif (OP)]

This also applies  for both coulomb's law and magnetism.
For  a wire when the circuit is closed the magnetic field starts to spread with the speed of light an experiment could be performed to determine whether magnetic field is already available at a point or it will reach that point after a time"it is not logical that the magnetic field already at infinity since we had a current started to flow at specific moment and shouldn't be available before that moment ,so how it would be available everywhere at an instant?"