Three-terminal hybrid transmission lines (TTHTLs) are attractive from both environmental and commercial view. Hybrid transmission lines are growing due to urbanization, connecting an industrial load and renewable integration. A TTHTL comprises sections of both overhead lines and underground/subsea cables or overhead lines with different X/R ratios. Faulted section identification (FSI) is key for defining the adaptive/selective auto-reclosing scheme and estimation of the fault location for TTHTLs. In this paper, FSI and fault location algorithms are proposed without using the parameters of any line section. Novelty of the methodology lies in a two-stage approach to the problem. In the first stage, series impedance parameters of all the sections are calculated using closed loop formulae. These parameters are then utilized in identifying the faulted section. In the second stage, the above calculated line section parameters and faulted section are used to estimate complete line parameters including shunt capacitance and subsequently the fault location. The advantage of the proposed method is that it does not require an initial guess of the line section parameters, is non-iterative in the first stage, and provides correct fault section identification for TTHTLs. These features make it suitable for designing the selective auto-reclosing protection scheme for the TTHTLs within traditional protection relaying hardware. More importantly, the series impedance parameters calculated in the first stage constitute good initialization values for the non-linear problem of estimating the complete line parameters. This results in better convergence of the algorithm and accurate parameter estimation. The developed solution is verified using the PSCAD/EMTDC simulations for TTHTLs connected with conventional and different inverter-based renewable resources. The performance of the proposed solution is compared with commercially available solutions, and it is found to be accurate. This solution is amenable for implementation in line differential protection relays without additional infrastructural changes.