The sand sifter star may or may not take to spot feeding - but one must hope you get lucky, as the majority are doomed to die of starvation in 9-12 months unless in a large system (over 100g) with little rock all in all (increase surface area of sand). You may see it losing pieces of its arm...or see hermits on it. Don't think it is being attacked - it is dying as most do. I personally would return it to the store. If you are looking for a functional deep sand bed, they are among the worst animals to add, as they eat the good critters in the sand bed. Try seeing if it will take to anything meaty - shrimp, squid, clams, frozen silversides. Put a bit on a bamboo skewer and put it right next to the arm and see if the star moves toward it to eat.
As for brittlestars -
The one to avoid is the green brittlestar, a known predator. It may or may not display this behavior in captivity, but it is a risk. Most others are not known to be as problematic, but could be, in theory (as could nearly every other animal we keep like shrimp, crabs, etc). I tend to feed mine a fair amount of shrimp pellets a few times a week. Throw them in there (but I have several brittlestars). It is really hard to judge exactly how much an individual should be fed I'm afraid. The daily bit plus a larger feeding a couple of times a week...that should be sufficient but really determined by the individual star and overall water quality.