Technically you can, personally I don't net any fish other than a damsel and that's only worst case scenario. Try your best to handle fish in a container, it doesn't mess with slime coat and also no chance of it getting stuck in the net. Hopefully you have a large enough container and you can fit it in the tank. Not sure how large of a fish and tank you are talking about though.
Hmmm that's tough, if at all possible I would still try and use a container.
If the container isn't feasible and or just stressing the fish out more chasing him then resort to the net. They don't always get stuck, but still avoid it as much as possible in the future.
To remove my lionfish and eels I used a 5 gallon bucket. I laid the bucket on its side on the sand bed and corraled the fish into it. I removed most of my rock and half the water to give me room to work and catch the fish quick. Not sure if that is an option if your tank is full of corals though.