Hi and welcome to the forum
The short green fuzzy stuff on the stem of the lucky bamboo is just green algae. Lucky bamboo is a terrestrial plant and its leaves need to be out of water. The stems will naturally develop algae on them when kept in aquariums.
The brown stuff is either diatoms or blue green algae (Cyanobacter bacteria).
All algae grow from excess light, or excess nutrients, or not enough live plants to use the light and nutrients. If you don't have many live true aquatic plants in the tank, you might have too much light or nutrients in the water for the plants you have.
You don't need to add carbon to aquariums with plants unless you are trying to grow terrestrial plants underwater. Then you need to have lots of light, lots of nutrients and carbon dioxide (
CO2). In an average aquarium, there is plenty of
CO2 produced all the time by the fish and bacteria in the aquarium. It's continually being produced all day every day, and normally provides plants with all the
CO2 (carbon) they need. There is also
CO2 getting into the aquarium water from the atmosphere.
Maybe post a picture of the entire tank and we can see how heavily planted it is.
In the mean time, reduce the carbon and other fertiliser, reduce the amount of food going into the tank (especially dry food), and maybe do a water change.
Regarding water changes, you should do a huge (75-80%) water change before adding more fertiliser. If the plants don't use all the fertiliser and you just add more each week, it can slowly build up over time and then suddenly poison everything in the tank. Doing a huge water change before adding more fertiliser will dilute any leftover fertiliser, and reduce the chance of overdosing.