In reference to the issue above, I was able to solve Problem #2 (subtotal being incorrect). This is related to the sorting order of the Order Total Modules. If I had the ot_coupon lower than the ot_tax (on the checkout page), then the ot_total was incorrect.

By changing the Sort Order so that ot_coupon was displayed higher (meaning it has a lower sort order value) than the ot_tax, that seems to have corrected the ot_total calculation.

I still cannot figure out WHY problem #1 is still happening: the coupon discount is being affected by something whenever it's used in a region with sales tax, even though I don't have sales tax being factored into my ot_coupon settings.