This study explores the complex phenomena involved in simulations of unsteady solid fuel particle combustion. These simulations use models that depend on parameters from experiments or small-scale simulations, making it important to quantify the sensitivities and uncertainties of predicted quantities. The study focuses on combustion under different freestream compositions, such as air and oxy-fuel atmospheres. The first step involves identifying the most sensitive model parameters, a process developed in a previous study. The framework is extended to study the evolution of sensitivities over time for a single unsteady particle undergoing devolatilisation. The dominant model parameters affecting particle temperature and burning rate are identified for both air and oxy-fuel atmospheres. The impact of different devolatilisation models on sensitivities is also examined. Additionally, an adjoint-based active subspace method (AASM) is employed to quantify uncertainties in predictions. The results show that uncertainties in particle parameters are much greater than those in gas-phase reaction rates. Furthermore, uncertainties are larger in oxy-fuel atmospheres than in air, emphasising the effect of freestream composition on model predictions.