I would say you will get away with filling that after applying hardener. As for the sill yes you can get a sill that is moulded as one for the bottom member of the frame and a separate type known as a loose sill and yes it will extend to the inside. At a guess because there seems some cracking of the paint where the sill meets the frame I would say yours is a loose sill but you can always have a poke around to verify that.

Richard