Hello sylvestris,
Sorry I somehow missed your post. The roots (and/or
nutrient solution) should not smell bad. If they do, that could be an indication that something is growing in your system that you don't want there (fungus bacteria etc.). For 4 gallons of water (nutrient solution) you could use just about the smallest air
pump available. Generally any fish tank air pump will say how many gallons it works for, I use that as a guideline. But more air bubbles never hurts anything, so I always try to get the biggest I have money for. And plants that don't like wet feet will benefit even more from all the air bubbles they can get in a water culture system.
As for the distance from the bottom of the net pots, that's something that varies from one person to another, plant to plant, and setup to setup. I like to make it adjustable and change it as the plants grow. Just touching the bottom of the baskets when they are small so the
growing medium can wick up moisture. Then drop the water level down as the roots grow down into the solution. But not so far that the roots cant wick up enough moisture to keep the growing medium in the baskets moist. The idea is to keep the exposed roots moist (as well as what's in the baskets), but not saturated. If the growing medium becomes too saturated that can even lead to stem rot. If they dry out then the plants suffer, but some plants tolerate wet feet better than others. I would say just play around with the water level and see what works best for you, and in your situation. Hope that helps somewhat, and sorry it's so late.