Who is Martha?
Martha is Castle's mom and she lives in his house with Alexis and him. She never mentions Castle's dad. Her job is being an actress but besides her saying that acting is in their family's blood, she doesn't mention it. But it's funny that her quirk is that she is sensitive about her age. :)
Picture of Martha
Picture found on http://www.abcmedianet.com/showcontent/primetime/castle/castle_i/sullivan.jpg
Who is she played by?
Character played by Susan Sullivan.