The large black and white snail looks to be a Citarium pica. Be warned, they eat a lot! In such a small tank one of those will likely need target feeding after a while. They also don't like high temperatures; IME they have always seemed more sensitive in that department than other similar CUC species like Turbo fluctuosa. If the tank is running over 78F then I would change species.
Might have to take the peppermint shrimp back though, I understand they can be a bit brutal to keep with some stony corals.
Missed this earlier, sorry. If you haven't already taken it back and the problem is picking at things, daily feeding with meaty foods or carnivore pellets like sinking shrimp pellets should remedy it. Most of the bad behavior they're accused of is the result of being kept in a state of desperation. They fight pest anemones more rapidly as such, but the unpredictability factor is also much higher.
On the other hand, if the problem is that is is going stompity stomp stomp all over something...that is harder to change, particularly in a small environment.
Any thoughts on why he might have died?
Any number of reasons for a snail death not long after purchase...sometimes very hard to diagnose. Some common ones:
- Sickly/stressed to begin with (how does the store keep its sw tanks? All in tip-top shape or...?)
- Shipping mishaps that do damage before the snail even gets to the store; sometimes the problems aren't obvious on new arrivals
- Too fast acclimation (skimmed through again but missed it if that was mentioned anywhere)
- Already old on collection (they are wild caught...no telling on age usually)
- Too high temp for the species (coldware species show up sometimes)
- Param swings associated with new tanks
- Became dinner for something
For the last one...I would not suspect a crab first necessarily, although they can be culprits. Often they aren't though and many get the blame unnecessarily even when present. There are many things that will eat a snail besides true crabs, such as hermit crabs (although again this is usually a sign something is off...hermits not being provided for correctly, etc.) and a small army of worms that can ride in as hitchhikers: Eunicid, Oenone fulgida, Polyclad flatworms, and even the odd species in the mostly safe family of Amphinomidae.
/www.youtube.com/watch?v=e2nuX446y3s
I was hoping so, someone else had suggested that they might be copepods to me as well earlier. Awesome news! 
