In Hindustani classical music, the tabla plays an important role as a rhythmic backbone and accompaniment. In applications like computer-based music analysis, learning singing, and learning musical instruments, tabla stroke transcription, $t\bar{a}la$ identification, and generation are crucial. This paper proposes a comprehensive system aimed at addressing these challenges. For tabla stroke transcription, we propose a novel approach based on model-agnostic meta-learning (MAML) that facilitates the accurate identification of tabla strokes using minimal data. Leveraging these transcriptions, the system introduces two novel $t\bar{a}la$ identification methods based on the sequence analysis of tabla strokes. \par Furthermore, the paper proposes a framework for $t\bar{a}la$ generation to bridge traditional and modern learning methods. This framework utilizes finite state transducers (FST) and linear time-invariant (LTI) filters to generate $t\bar{a}las$ with real-time tempo control through user interaction, enhancing practice sessions and musical education. Experimental evaluations on tabla solo and concert datasets demonstrate the system's exceptional performance on real-world data and its ability to outperform existing methods. Additionally, the proposed $t\bar{a}la$ identification methods surpass state-of-the-art techniques. The contributions of this paper include a combined approach to tabla stroke transcription, innovative $t\bar{a}la$ identification techniques, and a robust framework for $t\bar{a}la$ generation that handles the rhythmic complexities of Hindustani music.