Why would they need to do it in their own waters?

Because fish farms are generally stationary?

Is it not possible to build a floating farm in international waters?

The point is that a pen far away from the land might not be very practical/much more expensive to take care of

Seems like something that could be negotiated with other nations in a peaceful way, if fishing was the only concern. The sub fleet is the real concern though.

I don't know, but being stationary in deep water isn't trivial task. You can't just drop an anchor when you have 3000-4000m of depth below your feet.