Gravitational mass is actually a classical concept because it is the "charge" appearing in Newton's gravitational law. There is no analogue in general relativity.
First, in GR only spacetime is an unambiguously defined object. Space and time are derived concepts and they depend on how you decompose spacetime. This makes your questions confusing.
When you understand, you may reformulate your question.
If the irreversibility is a result of not being quasi-static, then none of T, S, P, V is well defined, and this equation fails.
If the irreversibility is due to friction, then obviously
{\rm{d}}U = T{\rm{d}}S - p{\rm{d}}U + \boldsymbol{f}\cdot\boldsymbol{x}
My point was that null surface as it is, the "speed" of event horizon is not a well-defined and physically useful concept. And you were trying to prove that the horizon is moving at the speed of light without defining the speed of a surface. It's not about the properties of event horizon; it's...