If they are 12 years old and are that size then their growth has been severely stunted by the size of the tank (which is not good, as it'll eventually kill them- you wouldn't keep a dog in a kennel its entire life? same reason why you should give large growing fish large tanks). You should really give them a larger tank, if only for the fact they will be suffering in there currently as it is. A healthy commet or common goldfish should be about a foot long (if not more) by 12 years old.
A Co2 system will incourage plant growth, but if you have an algae problem then that will get 10 times worse. The algae is there because there is already an excess of nutrients and/or light in the tank, more than what the current large plants are handling. The goldfish will also continue to eat the plants regardless of how well they grow and the plants will suffer for this- i know this from experience.
Simply put, unless you find a really hardy potted pond plant, your normal aquarium plants just aren't going to be able to grow well with goldfish in the tank unless you put something like a cage around them to stop the goldfish nibbling at them on a daily basis.
The other problem is that an excess of Co2 can suffocate fish, which is why properly run planted tanks with such Co2 systems tend to have very light stocking in them to help prevent this from occuring. Your tank is overstocked with very large waste producing fish, which would already demand a lot of oxygen in a tank that size- putting in a Co2 system will most likely suffocate the fish and cause an uncontrollable algae problem.
To get rid of the algae problem, completely avoid using any plant fertilisers or growth boosting stuff. The algae is there because the existing plants are either getting;
a. Too much light
b. Too many nutrients (like nitrates, or waste/poop produced by the fish)
c. Existng plants dying or are in poor health, allowing the algae to take over.
Or all three of these. Algae should naturally be kept in check by more evolved and larger plants in a good balanced ecosystem because algae is not that efficient at taking in light or nutrients and is easily outcompeted for resources by other plants. But when an inbalance occurs and there is too much of something in the tank (like nutrients for example), the algae is given an opportunity to bloom and grow out of control.
Adding an algae eater like some sort of pleco will not change/solve the algae problem, and could even make it worse in the long run as most omnivorous or herbivorous pleco's are big waste producers and will cause even more nutrients in the tank as they graze, which will contribute to the existing algae problem. Also, many pleco's only concentrate on algae when they are juveniles, and as they mature they can go completely off it and onto a more high protein based diet.
Not to mention the tank is already overstocked, adding more fish or critters would be irresponsable. So you need to adress the root causes of the algea problem to cure it. Test your water for nitrites, nitrates and ammonia, see how long the tank lights are left on per day, check out your tank maintanence/cleaning regime, remove dead or unhealthy plants from the tank etc...
Mussels in general can be quite bad for fish tanks. When they reproduce, their larvae swim out to find hosts after hatching and will burrow into the skin like parasites on animals like fish and live on the fish for a while before going through another part of their life cycles before finally maturing into mussels. Their larvae can kill fish or make them very ill, and their offspring often number into the hundreds or thousands and can be very unsightly.
But i think you need to ask yourself a very important question- are you bored with the goldfish, or the tank, or both?
Many people who overstock their tanks (knowingly or unknowingly) do it because they bore of their fish and concentrate too much on fish species appearances keeping them interested and occupied rather than what the fish itself has to offer. So far you have bought new inhabitants, but have done little to the tanks setup itself.
To get the most out of your fish, you need to give them a suitable and interesting habitat to live in. As silly as this sounds, goldfish can actually get bored of their environment. If the goldfish are bored, they will also appear uninteresting to you- when was the last time you sat down and just watched your fish for 10minutes or more? Do you like how the tank looks or find it pretty to view upon? Also, if the goldfish are stressed, they will not show the natural behaviour that makes each one so interesting and individual.
How often do you clean the tank in general on average and how often do you do it?
