There's no friction in space, It' s a vacuum. So you will continue accelerating forever if push is continually applied. It won't cost more power to push you just because you're going faster.
No that's not true actually, the density of matter in space is certainly low enough to not cause any noticable friction on anything we can launch at the moment, but once you start approaching an appreciable fraction of the speed of light it becomes significant. The actual estimate is about 1 atom per cubic centimeter which is not something we would need to worry about for current speeds, but even an atom can cause damage when it's striking a surface at close to the speed of light.
Oh yes, just a point, a perfect vacuum is only a theoretical possibility, even removing all atoms from an area doesn't provide a perfect vacuum because of electromagnetic energy and planck energy and as we all know E=MC2 so it's still not a vacuum even with no matter. It's rather complicated but if you could achieve a perfect vacuum, that is no matter, no energy, even planck energy the temperature would be zero K, and that according to current theoretical physics, is impossible, nothing can be zero K.