You can't explore the basement with a light source. There are two light sources in the Manor. A Lantern is located in Lady Jessica's Bedroom. An empty flashlight is located behind the password locked door in the west wing. Either will work. You will not need the West Wing Key to access the password door. You will need that key if you never found the password.
Yes but you don't need both unless you really want to open one chest in particular. That chest does does contain a very useful item but there is an alternative way to get the exact same item that I think is easier. Once you have a light source you can explore the basement and the corridor behind the locked door in the East Wing. You will find a way to obtain more than one item with the brush. Aside from the locked doors you can explore most of the West and East Wings no matter what key you create.