Hawkfish should be considered a danger to smaller inverts, snails for the most part should be okay but I would be wary with shrimp and crabs.
I've only had a longnose hawkfish by itself but I have seen some pairings in some tanks. I will say the longnose is probably one of the more interesting looking hawkfish, since it is pretty unique in body shape. All hawkfish sort of perch on corals/rocks/powerheads/etc. and like to keep an eye on their owners and what's going on outside the tank, so for that reason they're really neat to keep and watch.
They are probably best as one of the smallest fish in the tank, my little longnose hawkfish has started to bully my similarly sized Pink-Streaked Wrasse who he will eventually outgrow and probably need separating from for the wrasse's sake. I would also probably wait to add them to the aquarium last, unless you are adding something else that is super territorial and aggressive such as a damselfish.
The geometric pygmy hawk is a great starter hawkfish, they get along well in most tanks and don't get big enough to be able to consume large ornamental shrimp such as Skunk Cleaners and Flame Shrimp, that doesn't mean that they probably won't try at some point though.
I've never really heard of a hawkfish being a picky eater but that's not to say it can't happen. My longnose eats practically anything, even nori sheets. I would start out with some mysis shrimp or other chunky foods. After that they should start taking to other things such as flakes and pellets. If you do get a really picky eater, live glass shrimp or adult brine shrimp would be a good food option.
Aggression-wise, I do believe the flame hawks have more of a reputation as being a bully in the tank than the longnose. I chose my longnose mostly because he was only an inch long at the store and could grow up a bit in my 20 gallon. I love his coloration and personality, but I've also come to learn that they are not as likely to terrorize the whole tank and I will need to give him a bigger home eventually, which was all a part of my plan anyways
