At least for room temperatures the rock wool is assumed to behave isothermal. The soundspeed is much lower than in the air, about a tenth. There are impecance differences between the mineral wool and the sorrounnding air that can create reflections, and thus modal response. The sound absorption of mineral wool is well described by Mechels model. But I do not know the anwer to your real question if the transport mechanism is purely diffusive or also convective. I would believe convection can happen, and that the airflow resistivity in the mineral wool is essential in solving your problem, as it is for sound absorption.

First the thermal decomposition of resin is due to pyrolysis, the presence of oxygen is not required. The system is convective in the sense that volume of gas is created and transported to free surface, carrying oxygen outside material. If the entering heat flux is not too important one can suppose the convection quasi-stationary and the created gas in thermal equilibrium with fibers at any position in the material. Then the resulting problem is a thermal problem with source term. This source term is a result of a coupled equation for pyrolysis. This kind of problem is treated in my book "Ablative Thermal Protection Systems Modeling".

The pyrolysis is a pure thermal decomposition and don't need oxygen. When I say not too important fluxes that means less than 100 kW/m^2, typically.

Secondary reactions with the pyrolysis gas are possible. For example with oxygen diffusing from outside (depends on pyrolysis gas velocity flux) but also with oxygen created by resin pyrolysis. Moreover carbon deposition is possible: it is easy to verify this fact. You know temperatures, it is possible to infer chemical reactions in absence of external oxygen: decomposition pathway are known for many resins.