I would say It depends a lot of the type of apple and the final texture you want. Something like a granny smith or a honey crisp will hold their texture better. Something like a red delicious or mcIntosh will break down quickly. If you want the apples to hold texture add them towards the end and preference the former, if you want them to totally break down the later will be better.

I don’t think them breaking down would be very good though as they will not create a smooth sauce that I at least associate with a Japanese curry.

If you want them to carmelize and begin to break down, add them before any liquid. If you want them fresh and crispy, add them off the heat at the very end or even as garnish.

I think it depends on how mushy you want them to be - you could add them with the mushrooms if you don't mind them cooking down, but if you want them firmer you might adjust.

That said, I'm no authority on how to cook curry and don't have any sense of the "right" way to approach this according to a particular food culture.

Is this like a Japanese style curry? I'd probably put them in early so the meat has a chance to pick up the sugar, assuming you want them to break down fully into the sauce, which is the way I would usually do it. I usually don't cook a curry with meat that takes that long to cook, so I grate the apples.