rj45 transformer
well the transformer acts like a filter. It prevents DC signal to be received from and be transmitted to the ethernet line. and also it degrades the noise coming from the line.
For you second question, it's because the signal on ethernet cable is sent differentially. Transmission and receiving line each has a different pair of wires. They are usually shown as Tx+ and Tx- for transmitting and Rx+ and Rx- for receiving. that's why the center of the transformer is connected to the ground.