The Kilcher Homestead is a 600 acre Pioneer Homestead that has been protected for perpetuity via a ConservatIon Easement. The Kilcher Family has also preserved the Historic Cabin and site as a LIving Museum.
Yes, negative pH is possible, but not in water as a solvent. The range of pH in water is 0 to 14 (to be more precise, it is -1.7 to 15.7, but for simplicity's sake, we start with the usual values.) Thus, what pH indicates is the ability of the acid to form H3O+, which can then donate a proton.
So in this case, if Q is negative so is enthalpy. However, if you are at constant volume conditions (example: a bomb calormiter) where the pressure can change it is possible to have a V(deltaP) term that is greater than the negative Q (indicating the reaction is exothermic while still giving you a positive enthalpy.