If galaxies beyond the cosmological event horizon move faster than light is then that motion a combination of their KE and space expansion? If galaxies beyond the cosmological event horizon move faster than light is then that motion a combination of their KE and space expansion? Their KE alone isn't enough for them to move faster than light. But is this finite speed of an object simmilar to the motion of vibrations inside a material and that in that case the second reason of a so fast motion, expanding space could be simmilar to a evenly growing material?
 A: No galaxy moves faster than light. In cosmology there is a quantity called the recession speed which can exceed 299,792,458 m/s. But that isn't the speed of light when you're talking about recession speeds. Recession speeds are not measured in the special way that speed must be measured in order for the statement "the speed of light is always 299,792,458 m/s" to be true.
It's not true (as Buzz's answer claims) that light emitted by an object whose recession speed is larger than 299,792,458 m/s will never reach us. If there were no cosmological constant, all light would eventually reach us, no matter how large the emitting object's recession speed. With the measured cosmological constant, there is a cutoff distance beyond which emitted light will never reach us, but the recession speed corresponding to the cutoff isn't 299,792,458 m/s. (In the current era it's roughly 340,000,000 m/s.)
Space doesn't expand, at least not in the way that many people seem to think. Say Alice and Bob are both at the bottom of a symmetric crater like this one:

and climb out in different directions. The distance between them, which we'll measure along a line of equal altitude (not through the bottom of the crater), starts small but increases as they ascend. Would you say that they are stationary relative to each other, but the dirt between them is expanding? You could say it, if you carefully defined "stationary" and "expanding" to make it true. But it's a bit silly. The dirt isn't doing anything. The distance increases because Alice and Bob are moving away from each other, by any reasonable definition.
If Alice and/or Bob climbs diagonally instead of straight up, how does that influence the rate of change of the distance between them? Well, it is what it is. They end up where they end up, and you can choose how you want to measure the distance between those locations.
When they climb diagonally, is part of the change of distance between them due to the dirt expanding, and part of it due to their diagonal motion? No, unless you insist on being silly.
The large-scale shape of spacetime is not too different from the shape of that crater. The cosmological time is like the altitude, and the recessional speed is like the change of distance between Alice and Bob as a function of altitude.
A: The motion is primarily due to expansion. The KE is almost always irrelevant.
Imagine two objects with equal mass in a common circular orbit about their midpoint M. Assume that M is exactly at the point at which the expansion of the distance between the observers point O and the midpoint M is at the speed of light. Assume the orientation of the orbit is such that part of the line between O and M passes through the orbit as its diameter. Assume at this critical time one of the two objects has its motion close to towards the observer, and the other object has its motion close to away from the observer. Assume both objects are sending out high temperature light waves.
The object moving towards the observer moves at slightly less than speed of light towards the observer, and the light will travel at the speed of light towards the observer, but when it is seen when the wave reaches the observer, its wave length will be very much lenthened. The light waves from the other object will never reach the observer.
However, it will be a rather short time (how much needs to be calculated) after which the speed of both objects will be greater than the speed of light away from the observer.
