I suggest you read https://www.aquaticplantcentral.com/...ing-guide.html
for a simple, effective way of fertilizing the plants. I have found alternanthera reineckii to be a tricky plant - sometimes it grows easily, with nothing special needed, but other times it just won't grow at all for me. I also have had a difficult time getting it to grow well enough to avoid algae problems. It isn't supposed to be a difficult plant, but it also isn't a beginner plant. Until it is growing well I doubt that it can survive without added nutrients in the water.