The growing demand for integrating renewable energy into traditional power systems poses significant challenges, including intense transient dynamic simulations and uncertainties in parameter estimation. This contribution showcases how these tasks can be effectively accomplished, even with limited state measurements. We utilize Physics-Informed Neural Networks (PINNs) to integrate power system swing dynamics into the neural network training process, enabling efficient training on limited datasets with high accuracy. We evaluate the performance of PINNs in solving both forward and inverse problems on three benchmark multi-machine power system models: a 4-bus system, a 6-bus system, and the IEEE 39-bus system. The accuracy and computational efficiency of PINNs are assessed and compared with conventional numerical methods for each case.