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Quite probably gravitons can cause similar effects as photons. The reason I believe so is that gravitons arise by quantizing linearized gravity (linear approximation to GR), the procedure is very similar to quantization of electromagnetism. Individual gravitons have the usual relativistic energy and momentum relation to frequency (energy-density is ...

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One doesn't. We haven't even detected gravitational waves, much less single quanta of gravitational waves. As of now, gravitons are a theoretical idea derived by extending quantum mechanical ideas to general relativity.

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From what I understand gravity is similarly quantized and transmitted via gravitons. Well, we don't know that. There is no accepted quantum theory of gravity, only approximations like semiclassical approaches. We cannot give you a "mental picture" at the moment because we don't have one. We can speculate all day, and extrapolate from all the other ...

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Basically recoil, since photons can also carry momentum. The reason why this recoil can also lead to attraction instead of plain repulsion is that the exchanged virtual photon has a definite momentum, so it can not have a definite position at the same time (the position wave of a virtual photon is stretched out to infinity). The momentum can be transfered ...

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