A picture tells a thousand words, and so does Wikipedia
According to Wiki, it is normal for young fish to have external gills resembling that of an axolotl.
The gill filaments might have been damaged when the fish were at the shop or importers and have just grown back now. Alternatively the fish have developed them because the oxygen levels in the water are high enough so the fish don't need to use their lung to breath air from the atmosphere. (see under the heading "Description" at the following link.)
https://en.wikipedia.org/wiki/Reedfish
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I keep up on water changes every week and tank cleaning every month.
Weekly water changes are fine but what does your monthly tank cleaning entail?
You should use a gravel cleaner to clean the gunk out of the gravel every time you do a water change, (each week).
Power filters should be cleaned at least once a month and preferably every 2 weeks, once they are established (which yours is).
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You mention "dwarf neons". I assume dwarf neon blue rainbowfish (Melanotaenia praecox)?
If yes, these guys need clean tanks and plant matter in their diets otherwise they are prone to diseases like bacterial and protozoan infections.
Make sure you gravel clean the substrate each week and do a 75% water change each week to keep the aquarium clean.
Make sure any new water is free of chlorine/ chloramine before it is added to the tank.
Rainbowfish are sensitive to chemicals so be careful when adding tap water or treating the fish for diseases.
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Food for the reed/ rope fish can be any aquatic based food ranging from fish, prawn/ shrimp, squid, mussel, etc. Buy some raw or cooked prawns from a shop and keep them in the freezer. Take one out and defrost it, then remove the head, shell and gut (thin black tube in the body). Throw these bits in the bin. Use a pair of scissors to cut the remaining prawn into small bite size pieces and offer a few bits at a time. Your other fishes will eat this too so make sure it is small enough for them otherwise you could end up with bits of rotting prawn in the tank that will cause water quality problems. Wash the scissors and your hands with warm soapy water afterwards.
Same deal with fish, mussel meat, squid, octopus, etc. But a small packet of frozen fish and keep in the freezer. Take one out, defrost and cut the flesh (not the head or guts) into small bite size pieces. Offer a few bits at a time.
With the rainbowfish, they usually take Duckweed (a floating plant) and this can be grown in the main tank and the fish eat it when they are hungry. They also eat algae and soft leaf plants like Ambulia if they are hungry. Or you can blend up (cut up into small bits) spinach and add some of that to their food. You can also buy "Marine Mix" and "Marine Green Mix" from pet shops. They are prepared frozen foods made up from fish, prawn, and plant matter. You keep them in the freeze and take a cube out, defrost it and cut it into little bits.
I use to feed my rainbows a goldfish flake and pellet because it had more plant matter and less protein.