Hatchets are superb fish, but tricky. The smaller species (e.g. marble hatchets) are rather delicate and need soft, acid water and apparently live or frozen foods, not just flake. The larger species (e.g. silver hatchets) are more robust and forgiving. But still, as three-fingers says, soft/acid is the way to go.
I keep silver hatchets and find them to be very entertaining. They are surprisingly aggressive to one another (perhaps having just three specimens isn't sufficient?). No harm is done, but there is much chasing. The ignore the other fish mostly, the only fish they seem to interact with are the glassfish: the two species seem to "school" together some of the time. They inhabit the middle of the tank, not the top. The smaller hatchets do seem to be more surface-dwelling fish, by contrast.
Silver hatchets are incredibly greedy, and this seems to be a hatchet feature. They need a lot of food to stay healthy. Not sure why. Perhaps the large flight muscles use up a lot of energy, even if the fish aren't flying? Regardless, these are fish that will eat until they are bursting. They love bloodworms and small pieces of prawn and mussel. But they will also bite me when my hand is the tank! Quite a surprise!
In short, lovely fish, totally unexpected in their degree of entertainment, but slightly more difficult than the average "tetra".
I'd worry about the platy (needs hard/alkaline) and the betta (might get nipped) but beyond that these fish are easy to mix with anything. They even avoid my South American puffers.
Cheers,
Neale