The contact points on the Roomba may be dirty. Roomba's charging contacts are under the front bumper of the robot. This means that they are in front of the brushes, and see a lot of debris. They can easily get dirty and increase the resistance in the charging circuit. If after cleaning the contacts, the Roomba will still not charge correctly, you may need to replace the battery or get a new charging dock.

This is a fairly common issue with the iRobot vacuum cleaners. You may try plugging the charger into a different outlet. If the noise does not bother you, don't worry about it, it is not harmful to the robot. If you feel the need to stop the noise contact iRobot customer support.

The sensors that keep the Roomba from falling off an edge are called cliff sensors. If they sense open space below the Roomba, it will stop the robot. The issue with these is that they are sometimes triggered incorrectly. In the instance of your kitchen tiles, they are dark colored and look like an edge. The Roomba is designed to be able to determine the difference between a dark surface and an actual drop, but dirty or covered sensors can inhibit this ability. One thing to try is to clean the sensors with a cloth. They are the clear bars directly underneath the bumper. If that doesn't work you may have to replace the sensors all together.