So segwit transactions dont count the scriptsig in the transaction size. It makes segwit seem smaller but its actually slightly larger than P2PKH in terms of actual block space.
No, all parts of the transaction still counted. Although parts considered as witness data isn't multiplied by 4 when vBytes unit is used. You also may want to read this blog post,
Why a discount factor of 4? Why not 2 or 8?.