Nitrites are actually even more harmful to fish than ammonia is, and nitrates if they are too high can also be harmful to fish, from my understanding on nitrates anything higher than 40 ppm is considered too high and most people aim to keep nitrates no higher than 20 ppm, preferably lower. I agree with keeping water changes at once a week, I try to change at least about 30% of my water when I do a water change. By doing weekly water changes it will help to keep your nitrates in check, and will remove harmful waste from the water. Depending on how many plants you have in the 44 gal, they will help in controlling the nitrates. If you used a regular garden hose to fill the tank then it is very possible that something from the hose might have gotten into the tank.
If you are wanting to use a hose to fill your tanks I would suggest using something that is rated to be safe for drinking water, such as the hoses that they sell for the use of RVs, or something that is considered to be aquarium safe such as the hoses that come with the python or similar type of water changer (don't know if that is the correct term, but long day at work and brain is just not wanting to work to hard).
Also when you did your filter maintenance, and cleaned the sponge, how did you clean it? With sponges all you need to do is to squeeze them out in a bucket of aquarium water, easiest to do when you do your water chsnge. The idea is to get the gunk out of the sponge, but you do not want to thoroughly clean the sponge because you want to keep the benificial bacteria that is in the sponge. With the type of filter that you have I would make sure to never change everything at once. Also with sponges they can be used for along time, until they start to fall apart.
Wth the 10 gallon that you have your fish in right now, if it has not been cycled you will want to keep an eye on things as it goes through the cycling process, and you may need to do more frequent water changes. Also to help with the cycling process of the 10 gal if it is not already you can use some gravel from an existing tank that has been cycled. Just put some gravel into some nylon socking and place it into the 10 gal. Once the tank has been cycled you can remove the gravel and place it back into the other tank if you want.
Hope this helps, think I covered some of the major things I could think of, but like I said it has been a long day, unwind time