First thing, welcome to Tropical Fish Keeping forum.
Although I have not used these liquid carbon products, I have researched them. I have no intention of using them, due to not only the detrimental issues DKRST mentioned but also not finding it necessary.
On the first issue with respect to fish, it depends. Chemical substances that kill some plants, cause skin irritation, etc. are not in my view something to put into an aquarium with fish. Obviously these products if overdosed will kill fish. Not that one would likely overdose to that extent, but the point is that it has that capability.
On the second issue, plants require light and 17 nutrients to photosynthesize. These have to be balanced, and plants will photosynthesize full out up to the point where something is no longer available. The rate of growth depends upon the level of this balance. With minimal (but sufficient) light and all nutrients, growth will be healthy and steady, but usually slower. With more light and provided all nutrients are increased in balance, growth will usually be faster.
The aquarist can decide what he/she expects in the way of plant growth, and then provide sufficient light and nutrients to achieve that. If there are fish in the aquarium, they must be considered with respect to all this, as fish are affected by light to varying degrees.
Providing all nutrients are available and balanced to the light (intensity and duration), plant growth will be as healthy as it can be, but slower (though not always
). There is probably more CO2 produced in most aquaria than one might realize; I prefer relying on this natural CO2 rather than adding either CO2 or carbon via chemicals.