How deep could the Vredefort asteroid have penetrated?
10–16 km

there is an interesting equation that demonstrates an rocky impactor hitting rock does not penetrate further than its diameter. Basically because a meteorite and the rock it hits have similar density several things cancel out so depth of penetration maxes out at the diameter of a spherical projectile. 

Source 

Source 2


image from Wikipedia.

Here is more about impact craters in general. 
https://www.lpi.usra.edu/publications/books/CB-954/chapter3.pdf

Whether it hits on land or the ocean does not matter much either, although oceanic crust is thinner it is also denser, the mantle is even denser still so if it reaches the mantle it should penetrate even less than it would penetrating only crust. That said oceanic crust is only 5-10km in thickness so reaching the asthenosphere is completely possible. 

Also keep in mind the depth of a crater is different than the depth of the penetration, a penetrator can generate a temporary crater deeper than it penetrated due to shockwave deformation, much like how a you can use your finger to push a depression into a balloon without penetrating it at all.   

Would it fill with lava absolutely (at least partially) , just from the local rock melted from the impact alone.