Hi and welcome to the forum
Crayfish are best kept in a single species tank because they are nocturnal scavengers/ predators and will catch and eat fish at night. They also eat plants, which is good for them but not the best for a nicely decorated tank.
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Algae grows from excess light or nutrients, or not enough plants to use the light and nutrients. If you get lots of green algae growing on the glass and ornaments, then reduce the lighting time by an hour a day and monitor the algae over the next few weeks. You can also add some more live plants to the tank to use the extra light. Floating plants like Water Sprite will reduce the light getting into the tank and reduce the algae.
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What are the tank dimensions (length x width x height)?
What is the GH (general hardness) and pH of your water supply. This information can usually be obtained from your water supply company's website or by telephoning them. If they can't help you, take a glass full of tap water to the local pet shop and get them to test it for you. Write the results down (in numbers) when they do the tests. And ask them what the results are in (eg: ppm, dGH, or something else).
You have a list of fish that come from hard water (swordtails and platies) and fish that come from soft water (catfish, tetras, barbs gouramis). You need to know what the GH is before you get any fish because soft water fishes don't do well in hard water, and vice versa.
If your water is hard and has lots of minerals in (GH above 250ppm) then keep livebearers (swordtails, guppies, platies, mollies), rainbowfish or African Rift Lake cichlids.
If your water is soft and has no minerals in (GH below 150ppm) then keep tetras, barbs, gouramis and catfish.
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Regarding the livebearers, do not keep swordtails and platies together in the same tank. They hybridise and you end up with cross bred fish. And they are already messed up enough due to inbreeding at the fish farms.
If your water is hard and you want to keep livebearers, get a group of males or females but not both. If you want both sexes then have 1 male and at least 6 (preferably 10) females. This reduces the stress on the females. But find out what the GH is before you get any fish.