Do you have the little wire cable that runs along the bottom of your fence. If it is taut enough, your dog shouldn't be able to "push" under it.
I used a hack saw and was able to cut through them quite easily.
You would need to purchase a taller fence.
This bar is 5/8" wide. We do have 3/4" bars. They are available via special order in our stores. Thanks, Stuart MAT Customer Care
With a bit designed for steel, yes. I would use a punch to mark the spot so your bit doesn’t wander.