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Yes. The gravitational field couples to any energy; it doesn't care what the source is. Light carries energy, so the gravitational field responds to it.

Yeah, in physics if A affects B then B always affects A. This idea was first formalised as Newton's Third Law.

More formally, a photon field contributes to the so-called stress-energy tensor,which acts as the 'source' of gravity in the Einstein equations, thus affecting gravity, as you say.