Mandarins (I think they're not gobies by the way) need a well established tank with plenty of amphipods or copepods to eat, otherwise they'll starve. How old is your tank? One year is the average tank age to even begin thinking about Mandarins.
I've seen others say they sustain them with prepared foods, Cyclopeeze being one I believe.
And yes peppermint shrimps along with any other shrimp or crabs will eat dead fish.
Didja have any copper in the QT
? I'm not sure your mandarin would have fared well with that in his system. Even more, since there were probably no pods
in the QT
tank, he was probably on his way to starving before he got added to your main.