She seems to be adept at bending most earth materials including mud and metal. Since Lava-bending is a subset of Earth bending, can she bend lava and could it possibly be because of how good she is at Earth-bending?
No, Toph has not been shown to lava bend in any media to date.
Possibly. When Toph is introduced in the Legend of Korra, her cooking setup might be lava-based.
The full scene can be watched here. Notice how Korra's flame produces dynamic light, but whatever is under Toph's pot only produces a dim, constant light.