How to monitor switch state?
To get the functionality you describe, you need to have "3-way" (SPDT) switches &mdash; a manual one and a relay that the Arduino controls. This is just like having two switches that control the lights from either end of a hallway, except that one of them is controlled by your MCU.

Sensing the state of the light is a separate matter. There are many circuits on this site and others for safely detecting the presence of line voltage at the light socket.