Refer to the SB equations...Set T1 and T2 to the same number...P=0 no energy exchange regardless of how much bad math you engage in to torture the equation in an attempt to satisfy your belief.
No heat exchange. For energy exchange by radiation there is always radiation produced by both objects, leaving a net flow that is considered heat exchange.
Photons only interact with matter, they do not cancel out during the journey from emitter to absorber.