Electric aircraft represent a promising low-emission alternative to fuel-powered aviation. As the energy source, the battery pack must guarantee key performance metrics such as energy density, power density, lifetime, and safety. Among these, energy density is particularly critical as it directly impacts the range and payload capacity. Additionally, the battery thermal management system (BTMS) of the battery pack is essential to maintain safety, efficiency, and lifetime. Hence, to design a battery pack with improved energy density and optimized thermal and aging performance, a complete electro-thermal-aging (ETA) model at both cell and pack levels is developed to predict pack behavior under operational conditions. Simulations demonstrate that the proposed model achieves an accurate thermal prediction accuracy within 0.87°C during an example all-electric aircraft (AEA) mission profile. Optimization based on the proposed model is conducted, focusing on geometric configurations of the battery pack and coolant flow parameters, including channel wall thickness (L_Al), inlet width (W_cl), cell spacing (D_cell), package wall thickness (L_enc), inlet flow temperature (T_cl,in), and flow velocity (U_cl,in). An optimized liquid-cooled battery module using Samsung 18650-35E cells is designed with [L_Al, W_cl, D_cell, L_enc] = [0.4, 1.6, 20, 0.5]mm, T_cl,in =35°C, and U_cl,in = 0.05ms^-1 during cruise and 0.02ms^-1 during takeoff, climb, and descent. This configuration achieves a maximum temperature of 41.76°C and a maximum cell-to-cell temperature difference of 3.11°C, improving thermal uniformity. The lifetime performance also demonstrates a 5.51% improvement in state-of-health (SOH) after 180 cycles. Based on the module-to-pack structure analysis, the battery pack exhibits energy densities of 227.01Wh kg^-1 gravimetrically and 353.67Wh L^-1 volumetrically. This study facilitates the guideline for compact and lightweight liquid-cooled battery pack design with improved thermal and aging performance for AEA applications.