Is it possible to create a portal through another portal in Co-op?
No. There is never any case in Portal 2 where you can send a portal through another portal. As you noticed, shooting a portal at an existing portal replaces the existing portal. The behavior you are describing would be inconsistent with that, so it cannot happen.
Nope, the game does not allow this, you will at most just end up placing another portal in the same spot.