Since vanilla gateways don't allow the other empire to travel to your other gateways, I don't see why emergency gateways are different. So when you capture your enemies' emergency gateway you can just travel to their other emergency gateways, which seems unfair given that you cant deconstruct them.

You should also be able to build emergency gateways in the system with a gateway. Since you can still build a gateway in a system with an emergency gateway, I don't see how the opposite is not possible.