Room acoustic parameters (RAPs) and room physical parameters ( RPPs) are essential metrics for parameterizing the room acoustical characteristics (RAC) of a sound field around a listener's local environment, offering comprehensive indications for various applications. The current RAPs and RPPs estimation methods either fall short of covering broad real-world acoustic environments in the context of real background noise or lack universal frameworks for blindly estimating RAPs and RPPs from noisy single-channel speech signals, particularly sound source distances, direction-of-arrival (DOA) of sound sources, and occupancy levels. On the other hand, in this paper, we propose a novel universal blind estimation framework called the blind estimator of room acoustical and physical parameters (BERP), by introducing a new stochastic room impulse response (RIR) model, namely, the sparse stochastic impulse response (SSIR) model, and endowing the BERP with a unified encoder and multiple separate predictors to estimate RPPs and SSIR parameters in parallel. This estimation framework enables the computationally efficient and universal estimation of room parameters by solely using noisy single-channel speech signals. Finally, all the RAPs can be simultaneously derived from the RIRs synthesized from SSIR model with the estimated parameters. To evaluate the effectiveness of the proposed BERP and SSIR models, we compile a task-specific dataset from several publicly available datasets. The results reveal that the BERP achieves state-of-the-art (SOTA) performance. Moreover, the evaluation results pertaining to the SSIR RIR model also demonstrated its efficacy. The code is available on GitHub.