You asked two questions.
1) What is the speed limit?
2) Why is it assumed that light is the fastest thing in the universe, re travel?
You answered the first question yourself by saying that: "There is no limit in space," the thing though is that the meaning of the word "space" is misunderstood by most people including scientists.
The fundamental meaning of the word "space" is a concept of a volume (3D area) that is totally empty, in other words, such a volume does not contain any energy or fields of any kind.
Such emptiness does not exist in our known universe for any measurable length of time.
The assumption that light is the fastest thing in the universe is based on several misconceptions.
First; it is assumed that light has no mass, second; it is assumed that light that travels to us from the countless stars in the universe have traversed through empty space, and third; it is assumed that mass and energy are one and the same as far as effects concerning speeds that are near or equal to that of light.
Despite the popular belief to the contrary, the light photons are made up of the same material as that which mass is made of.
The space between the planets and the stars is not empty in any sense of the word, even if all the gas particles and protons and electrons that are in the said volume were taken away, there still would be all the photons of light coming from the countless star systems. (photons are something after all.)
The space between the stars is full of photons travelling at a certain speed, if an object is pushed to the same speeds as the photons, then the object will meet extreme resistance from the photons that will impinge against it.
The effect is somewhat analogous to the "terminal velocity" of falling objects.
A free falling object achieves its terminal velocity when the downward force of gravity (Fg)equals the upward force of drag (Fd). This causes the net force on the object to be zero, resulting in an acceleration of zero. ...
en.wikipedia.org/wiki/Terminal_velocity
So, in "empty" space it is possible to go much faster than light but such emptiness does not exist in our universe.