Assuming a "Tax" is an extra percentage amount on money paid in exchange for goods/services: no this would not tax people for breathing, unless you know of someone who already pays for the privilege of breathing.

I have to pay the sewer department for crapping. I get fined for crapping where I’m not supposed to. You pay for externalities where it matters.

I'm fine with that. Breathing is a negative externality. If someone were to actually include breathing, it'd be an incredibly small amount relative to other human activities.

No, it wouldn’t as breathing is basically carbon neutral (on largely vegetarian diets).