Sounds like an interesting build, can you share details? I suspect it will be quite a challenge to get all the electronics to work, but those motors are really quite fantastic.
Unfortunately I don't really have input to provide on the gearbox question, I don't recall hearing of the oil cooler failing (at least not a common problem as far as I am aware), I suspect it would depend on how long ago it failed and how long it was driven like that. Potentially the pressure in the box will stop water from flowing in but allow oil to flow into the radiator. But I don't know for sure.
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