Is empty space a pure vacuum?
Space isn't empty and it is not purely vacuum.
Space is never a pure vacuum. Interstellar space contains hydrogen, helium and other lighter elements. They are quite disperse but it isn't a true vacuum.
Also, due to quantum effects virtual particle/anti particle pairs get created spontaneously in a vacuum. These particles annihilate each other soon after creation.
If a region of space is near an object with mass, it will be curved in 4 dimensions. Particles will follow geodesics in space-time if not under the influence of an external force.