Just to add a bit of info on the "forget about cycling the tank" bit.
Your ammonia test is actually testing for Total Ammonia Nitrogen (TAN). This is a combination of free ammonia and ammonium. It's only the free ammonia that is toxic to fish.
The proportion of free ammonia and ammonium is temperature and pH dependant. As these 2 parameters rise, more of the TAN is free ammonia and less of it is ammonium. The reverse happens as these 2 parameters fall. Free ammonia turns into non toxic ammonium. At pH below 7 you can pretty much say that all the TAN in your test is ammonium. You can certainly say that if your pH is as low as 6.
This is a thread on ammonia toxicity if you want to learn a bit more.
*WARNING* This guide is intended to give a better understanding of Ammonia toxicity and is not intended to diagnose or treat any problems. Please use this information wisely. *WARNING* Ammonia. It's bad. I think even the most novice fishkeeper understands this concept. It's a common idea that...
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So, while it may not be possible to cycle an aquarium with very low KH, because low KH will be reflected in a low pH it doesn't matter too much if you arent cycled. What you would have to watch out for is if pH rises without you knowing. As you wouldn't be cycled ammonia will build up. At low pH this is going to be non toxic ammonium, but if the pH rises then ammonium will become toxic free ammonia.
Not all fish are going to appreciate such a low pH/ low KH environment. So if you go down this route select your fish species carefully and have a good acclimating process as any fish you buy may not have been bred in such acidic conditions.
The other side of this is, if you decide to artificially raise the KH and pH, you need to keep on top of that. There are salts you can buy, that raise KH or you can have calcium carbonate features in your aquascape to raise the KH, but monitor things because if the KH gets depleted for any reason, then your cycle would cease to function.
This might also be a factor in your poor plant growth. Aquarium plants tend to do better in water with some KH in it.