If you turn off your filter, you might as well clean it out because by the time you use it again, you will have created a toxic condition inside your filter box that can kill off the fish once you turn it back on. Gouarmi do prefer to spawn in slow moving to stagnent conditions so if you trying to breed them you should turn off the filter.
Hope this helps
)Yes. You will probably have the filter off for a couple of months so the beneficial bacteria will die off and decay so the cartridge will be worthless.
Another choice would be to use a bare, empty tank with new water, some plants and no filter and let them spawn in there. Once the fry have started free swimming and eating, you can add a sponge filter to the setup. (This is a better way of breeding anabantids BTW
) They just put a pair of fish in a plastic bag lined styro box with a plant in the water for the nest. No filters, no airstones, gravel or anything. That's how little is necessary for breeding gouramis.Being a Labrynth fish, Gourami's don't need the oxygen from the water. Just make sure that the airflow is weak as to not disturb the nest. Also, Labrynth fish fry don't like moving water all that much so you need to be aware of the water movement.
When I was at the fish farms in your backyard ( in Tampa
Good luck with yours. Keep us posted
: Labrynth fish ( Bettas, Gouramis, Paradise fish, etc) have a special gland/ organ called a Labrynth which enables them to take air from the atmosphere and convert it into oxygen for their blood. In other words, they are supposed to be coming up to the surface to breath. If this were a non Labrynth fish, this would be a bad thing to see but in this case, totally normal. They have been doing it the whole time you just may not have seen it. Be educated 
