Brake fluid is under pressure in the braking system of the car. By the ideal of actually pressurizing the fluid like you would a gas, that can not be done. I believe that you are actually hitting upon the idea of putting the fluid under pressure like moving through constricted areas very quickly. As for actually pressurization, there is no possible way to do this with an actual fluid.
YES, all fluids are infinitesimaly compressible. as proven in any hydraulic system, the only limit to this compression is the container in which the fluid is held. :) A "hot "fluid is thinner and more easy to compress that's why a cooler is added to most pumped hydraulics.