There is no full list of characters that are appearing at Disney World on any particular day. The list of character appearances varies daily. Many of the regularly scheduled characters appearing in each park are listed on that park's Times Guide (free, located near the maps at the park entrance), but there will be other surprise characters in the parks as well. Also, if you or your child has a favorite character, you might want to look into whether that character is part of any of Disney's wonderful character dining experiences. This is great way to get some quality time in with a favorite friend.
Nearly all the characters will sign autographs, with the exception of the few whose hands or other extremities are such that they cannot physically hold a pen.
If there is a specific character that you're looking for, you could always stop by the Guest Relations office at any of the theme parks and ask them to call the "character hotline" for you. They will be able to tell where and when a specific character is appearing at the time of your visit.
For a list of some of the characters that you are very likely to find in the parks, you can read the answer to another guest's question
HERE.