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I want a higher resolution ADC than the Arduino provides. Would it be legal to use a 12bit i2c ADC and connect that to the Arduino?

If only 12bit, you can use Arduino DUE.

i assume i would be allowed to use something like the stm32 blue pill instead of an arduino

I asked FAQ about external ADC, the answer was no, then changed to not very clear.

I will allow you to use the stm32 and external ADC if I run the event. But, please if possible, make the ES's life easier.