So, why isn't that face filled properly? and how can I fill it smoothly?
by selecting the edges and just pressing F you are creating a so-called n-gon (face with more than 4 vertices). The subdivision modifier can't handle those very well and thats what messing up your mesh.
Select the top and bottom row of vertices (1st image) and use grid fill to make the faces.
Mesh ‣ Faces ‣ Fill/Grid Fill
Result on my mesh: (your proportions are a bit different, but its basically the same structure):