Plants will always grow if they have enough light, and a source of nitrogen, potassium phosphorous, carbon, calcium, magnesium, and several trace elements. That suggests that your plants don't get at least one of those requirements met. I assume you have a 29 gallon tank, because the light you have is only 24 inches long, too short for a typical 30 gallon tank. The standard 29 gallon tank is about 18 inches high. Two T8 bulbs, assuming they are not old bulbs, should be giving you adequate low light, but near the minimum required. Carpet plants grow at the substrate level, where the light intensity is the lowest, and it is those that aren't doing well. So, I suspect you don't have enough light for them. If the bulbs are over 6-8 months old, replacing them might help.
Algae require such minute amounts of nutrients that they cannot ever be starved. If you have light you will have some algae. You should be able to wipe the glass sides weekly and take care of most of it that way. Algae tend to grow best when the plants aren't healthy, so getting them growing well will help a lot with getting rid of algae.