Nitrate is not a problem in small amounts like that. I would keep an eye on the nitrite. If it starts to rise, you will need to do much larger water changes.
No, less stress due to proper shoal size is a much more minor thing that the kind of major survival stress that would hit the initial tetras that are in there now if the tank is not cycled and begins to show traces of ammonia and/or nitrite. It can take many days for these traces to first start to show up in a new situation, so you have to give it at least a week or maybe two before feeling you actually may know the real situation with the water chemistry. Tanks and water chemistry are a much slower changing thing than beginners first realize. Besides the filter possibly being not cycled at all, there's the possibility that the mature media transfer will not fully "take." Its rare but it does happen sometimes, so that's also one of the reasons for being patient and watching the test results over the week or more.
The whole hobby is all about slowing down and relaxing more in life. There's no real need to rush the setup and buildup of fish and plant stocking as they are one of the more active and pleasurable aspects of the hobby and the chance to observe and learn should be savored. You sound to be doing things right, so a good tank setting should eventually be yours to enjoy.
~~waterdrop~~

Every 1 ppm of ammonia that is converted to nitrate becomes 3.6 ppm of nitrate. That means big numbers in a hurry all the time during a fishless cycle. A fish-in cycle should not have a big enough stocking for rapid rises in nitrates, but ti can happen. You might want to have a hard look at how much you are feeding. Any left over food in the tank is a source of nitrogen along with fish waste, which is more abundant with heavy feeding.
Agree. Some catfish have even been shown to do ok in 1000ppm. I think it varies a lot by species - some say that GBRs, for instance, are pretty sensitive to it. 40ppm is nothing to really worry about. WD40ppm of nitrate is fine, levels of up to 400ppm are safe.