Turning our 'suspension of disbelief' fields to max, I'm going to assume that a large measure of handwavium is stabilising this atmosphere and have a bit of fun.
How would this atmosphere affect photosynthesis? It would render it completely irrelevant.
With a few changes to known biologies, you've just created a 'soup in a can' of atmosphere. Assuming you have the ability to metabolise hydrocarbons directly (that's what methane is after all) you take your CH4 (methane), 2x O2 and you create water and carbon dioxide while at the same time producing energy. You've got a breathable atmosphere that can give you energy at the same time.
The reason for this is the same as the reason that the atmosphere is really unstable; biological energy production takes advantage of the same exothermic reactions (in controlled and measured amounts) that make these chemicals want to go boom in the first place. This is why fertiliser is so useful as an ingredient for explosives as well. The chemical reactions that release so much energy at once are not that dissimilar to those that happen in organic bodies constantly on very small scales.
Your problem here is that eventually, WITHOUT photosynthesis, your life forms will convert all the O2, and a reasonable proportion of the methane into water and CO2, and you need photosynthesis after all.
Such a planet (again assuming a handwavium approach to keeping this atmosphere stable in the first place) will probably develop simple life forms that will 'eat' the atmosphere, converting it to a mix more in line with early Earth, and generating water at the same time. That life will eventually die out, and the next wave would start with plants that use heat to generate the endothermic reactions of photosynthesis. Heat and light are basically the same thing if you take eyes out of the equation so this second generation of life would likely be similar to what we would expect to see on Earth, except that it may well still be designed to consume methane instead of carbohydrates. That means that the animals that eventually predate the plants may well ALSO have their metabolisms designed to consume methane, meaning that they predate the plants for nutrition more than energy, which they can get from the atmosphere.
I would stress that this is all speculative, and is based on the existence of an impossible situation in the first place. That said, it could be a very different world because food as a concept may be designed around trace elements rather than energy generation, meaning it could be a very small amount of predation that is limited to plant life (no carnivores) so as to maximise mineral nutrition by consuming plants that leech it from the ground very effectively.