Welcome Rodo!
Chara usually has a skunky or garlic smell if you squeeze, crush, and/or tear it. The submerged stuff you mention that is floating up in clumps sounds like filamentous algae (aka FA). The first thing to do is positively identify the vegetations/algae. Pictures will help the forum to identify the types. These pics will need to be very clear and particular to get the best advise. It is helpful to take a clear glass baking pan with enough clear water (tap is fine) in it to allow a sample of the greenery to "fluff up". Put this pan on a white surface and get some photos to post. Using a very clear plastic bottle, jar, or baggie works well too (with a white background also).
I would not do any treatments without knowing what you are dealing with for sure. And, adding more carp should wait as well. FA is not a favorite food for carp unless it is a last resort and even then they may not do much about it.
In my opinion, aeration is a small tool in pond management and plays it's biggest role in increasing dissolved oxygen which allows for more fish mass to live in the pond. A quick web search on weed/algae control produces many hits of aeration sellers claiming it will solve all your problems, but that's just not true. It will help, but it's a small piece of the big puzzle.
I can not help with the water dynamics you are experiencing, but there a quite a few folks here that will chime in.
