The nature of dark matter is a crucial problem for both cosmology and particle physics. The weakly interactive massive particle (WIMP) is one of the top dark matter candidates searched for decades because of the so-called `WIMP-miracle'. Dual phase liquid xenon time projection chambers (LXeTPCs) have led the most sensitive searches on the GeV-scale spin-independent WIMP-nucleus scattering cross section for years because of the strong background suppression and scalability. With 3.7 tonne liquid xenon in the sensitive region of the LXeTPC, the Particle AND Astrophysical Xenon (PandaX) collaboration is now running PandaX-4T experiment at the B2 Hall of China Jinping Underground Laboratory after the PandaX-II experiment. The strongest limit back to the release time was published with the 0.63 tonne$\cdot$year exposure on the standard thermal WIMP search with a lowest excluded cross section (90% C.L.) of $3.8 \times10^{-47}$~cm$^2$ at a dark matter mass of 40~GeV/c$^2$.

In this thesis, I discuss research and developments correlated to PandaX experiments. I present the whole procedure of $^{83}$Rb/$^{83m}$Kr calibration in the PandaX-II detector from sources production with 3.4/20~MeV protons bombardment on natural krypton to the data analysis after injection into the PandaX-II detector, which becomes crucial for the increasingly larger detectors. With the $^{83m}$Kr events, I present the developments on the horizontal position construction algorithms in PandaX-II, which is important to fully take advantage of the self-shielding ability of xenon, determining the fiducial volume directly related to the exposure. Moreover, I discuss the procedure of the profile likelihood ratio analysis to set the limits and sensitivities, where probability distribution functions are prepared with reweighting Monte Carlo to handle the systematic uncertainties in the detector response modeling more robustly. The methodology is applied on the spin-independent WIMP search to prove consistency with the template morphing method. Then, I conduct a search on electronic absorption of sub-MeV fermionic dark matter which shares similarities with sterile neutrino dark matter. Such dark matter with a 60~keV/c$^2$ mass can explain the low-energy ER excess reported by XENON1T collaboration, but is only marginally allowed by our constraints.