Is there a FOSS embedded OS, like LEDE or something like that, for the Zyxel AC750 NBG6515 router? I see the NBG6616 on the list but that is clearly a different model.

I'm not seeing the 6515 model on the lists of supported hardware for LEDE and others, so I expect that it is not supported.

Along the same lines how can I find information about the chip sets used in that model of router?

Knowing those would give me more of a clue. Unfortunately the corporate web site [1] has a web page for that model that is infested with javascript and, even when the JS is activated, does not provide any technical information. There is even a foldout for "Hardware Specifications" which says nothing meaningful about any aspects of the hardware.

Where should I be looking?

[1] The Zyxel web site clearly required a lot of work to achieve the sorry state it is in. Such poor design comes neither by accident nor without great effort. They only need to add Adobe Flash dependencies to take it to the next level.