>>1995(Rest) mass is absolute:
m^2 c^4 = E^2 - p^2 c^2
m is (rest) mass, c is the speed of light, E is energy, p is momentum.
If you want to convert kinetic energy into another form, you need to preserve momentum too. This means you have to cancel it out using an opposite momentum. If you switch reference frames, that other particle changes kinetic energy too, so that it all works out.
>>1992>>1994Actually, general relativity doesn't preserve energy. The cosmological constant, a.k.a. energy of the vacuum, can create energy out of the wholecloth in a way that enforces itself exponentially^1 . Also, radiation (and fast-moving particles) lose energy as the underlying spacetime expands.
[1] However, this energy is always at maximum entropy and thus you can't do work. Unless inflation is correct, but that's another story.