If we have a Newton's cradle toy where the balls actually touch each other. Can energy be transferred from the first ball to the last one faster than the speed of light? And what factors control the energy flow in such case?
Any energy transfer from collisions between the balls won't be transferred faster than light. It will be transferred at the speed of sound within the metal, which is much, much slower than the speed of light. For example, for solid steel balls, the speed of sound is roughly 5900 m/s, so a collision at one end of a 5-cm-long chain of steel balls will take around 8 microseconds to propagate to the other end - detectable with advanced high-speed cameras.