I've had one in my tank for about 2 years. It definitely will kill hermit crabs and shrimp, even cleaner shrimp. It may also peck at snails, especially fleshy ones like nassarius, though I don't think I've ever seen mine kill one. Astreas seem nearly impervious to this wrasse though. They're too well armored. I still have dozens of astreas and haven't bought any in over a year.
Mine will not tolerate other wrasses unfortunately. He killed a fairy wrasse. He also doesn't like sand dwelling gobies and will harass them to death as well. Same goes for jawfish.
They should be totally fine with other common reef fish like tangs, clownfish, angels, anthias, mandarins, etc. They don't bother corals, though they will flip loose frags over in search of food.
Edit: If you already have wrasses in the tank, it's likely that the red coris will get along ok with them. I had a melanurus wrasse in the tank when I got mine and they were the best of friends.