The breakthrough in the barrel channel is common, not ideal, but common.
I wouldn't worry too much about the gap at the rear of the tang. Having a slight gap there is actually preferable. Once the stock is finished, it will be less noticeable. More importantly if there is not a slight gap there, there is a high risk of wood chipping out behind the tang due to the recoil of the rifle. The thickness of a couple sheets of paper worth of gap is enough.