Yes you can sawcut the asphalt to a shape you'd like. Just be aware that you do not want to drive right on the edge so I don't know how much more you would extend the landscaping beds/grass. You will also probably have a base of a handful of inches of gravel to remove and replace with topsoil if you want to grow something. As far as the tree roots, the drive was probably there first, removal of tree roots of that size under the canopy can have consequences for the tree. As far as condition, review that yourself or by your inspector and account for that in your offer, if you want.