LHCb RICH and VELO upgrade studies and measurement of the ratio of branching fractions $BR(\Lambda_b^0\rightarrow\Lambda_c(2625,2595)^{\pm}D_s^{(*)\mp})/BR(\Lambda_b^0\rightarrow\Lambda_c^{\pm}D_s^{(*)\mp})$

Particle physics seeks to study the fundamental building blocks of the Universe by understanding the laws that govern their interactions. In recent years, the LHCb experiment has established itself as a world leader in flavour physics, a success attributed to multiple factors. Achieving precise Physics measurements requires not only sophisticated data analysis but also a detailed understanding of detector operations. Furthermore, ongoing research is essential to equip the experiment with cutting-edge technologies that enhance its measurement capabilities. \\ This thesis includes all of these aspects. Using LHCb Run\,2 data, it presents a measurement of the branching fraction ratio $BR(\Lambda_b^0\rightarrow\Lambda_c(2625,2595)^{\pm}D_s^{(*)\mp})/BR(\Lambda_b^0\rightarrow\Lambda_c^{\pm}D_s^{(*)\mp})$, an as-yet unobserved channel that is crucial for investigating the lepton flavour anomalies identified by the LHCb experiment. For LHC Run\,3, the LHCb detector has undergone a comprehensive upgrade, followed by an extensive commissioning phase. This thesis details studies on the gain of the LHCb RICH detector's photosensors, which directly impacts the experiment's particle identification capabilities. Looking ahead, the future success of LHC experiments depends heavily on the timing performance of their detectors. A dedicated R\&D program aims to achieve a time resolution on the order of 150 ps for the RICH detectors to manage the increased instantaneous luminosities expected in Run\,4. The time resolution estimation is performed as part of this work. Finally, as we approach the High-Luminosity LHC era from Run\,5 onwards, this thesis also explores the potential of innovative 3D silicon sensors for precise time and spatial tracking.