Is the Higgs field part of space? So I looked for some explanations, how I understand it so far is that the Higgs field causes particles to have mass by drag, like drag force in water, which prevents objects from moving at the speed of light, is that correct? so is the Higgs field essentially an element that makes up space?
 A: The Higgs field is in space (time), space is not made of it. Like any other field, mathematically it is a function that takes a value (usually a number) at each point in spacetime.
Now, for most fields the default value is zero. By "default" I mean the state of least energy; if you want a nonzero value you have to put energy in. The thing about the Higgs field is that its least energy state is a definite nonzero value. This in turn implies that if any field is coupled to the Higgs, it will experience a sort of constant interaction, which manifests itself as a mass; this mass is related to the strength of the interaction.
A: Higgs field as I understand is everywhere. 
The interaction of an elementary particle with higgs field gives resistance to accelerate, is what we call mass.
Some particles simple does not interact with higgs field (photons, gluons) and they have no mass.
Heavier particles interact more.
As long a particle becomes closer to speed of light more energy is necessary to accelerate it. Infinite energy is necessary to accelerate it if it is infinitely close to speed of light.
As I understand, Higgs field give mass, accelerate a particle is linked with special relativity, and I don't think both have a direct relation.
