That's a lot of questions
I'll try to cover everything important!
I wouldn't bother separating the fish; the ammonia produced by a few small tetras will be negligible, compared to the plec. Get the plants straight into the tank with the fish; they will help absorb some ammonia and nitrite to stop it building up. I also wouldn't bother trying to fishless cycle the small tank (unless you want to do one for the experience). Once you have one cycled filter, if you need another cycled tank, you can just take a some media from the cycled filter and put that in the new filter.
Use the plant fertilizer according to the instructions. The Nutrafin Cycle is unlikely to do any good, as it doesn't contain the correct bacteria, but you can use it, again according to the instructions, if you have it, as it won't do any harm.
You need to test the water in the tank at least once a day, to monitor the levels of ammonia and nitrite, so you know how much water to change.
The blackness from the carbon pouch was probably because it split or wasn't rinsed properly; carbon can be very dusty.
Cleaning a filter is really quite simple. Do it once a week, when you're doing a water change. Once you've taken the water out of the tank into your bucket or jug, or whatever it is you're using, take all the media out of the filter, swish it around in the old water to remove the worst of the 'gunk' and pop it back in the filter. The bacteria will survive for quite a time out of water, but you don't want to ever let it dry out. It's best to get it back in the filter again straight away.
I wouldn't bother separating the fish; the ammonia produced by a few small tetras will be negligible, compared to the plec. Get the plants straight into the tank with the fish; they will help absorb some ammonia and nitrite to stop it building up. I also wouldn't bother trying to fishless cycle the small tank (unless you want to do one for the experience). Once you have one cycled filter, if you need another cycled tank, you can just take a some media from the cycled filter and put that in the new filter.
Use the plant fertilizer according to the instructions. The Nutrafin Cycle is unlikely to do any good, as it doesn't contain the correct bacteria, but you can use it, again according to the instructions, if you have it, as it won't do any harm.
You need to test the water in the tank at least once a day, to monitor the levels of ammonia and nitrite, so you know how much water to change.
The blackness from the carbon pouch was probably because it split or wasn't rinsed properly; carbon can be very dusty.
Cleaning a filter is really quite simple. Do it once a week, when you're doing a water change. Once you've taken the water out of the tank into your bucket or jug, or whatever it is you're using, take all the media out of the filter, swish it around in the old water to remove the worst of the 'gunk' and pop it back in the filter. The bacteria will survive for quite a time out of water, but you don't want to ever let it dry out. It's best to get it back in the filter again straight away.