THEY ARE NOT ALGAE EATERS... in the sense we are using the term (eg like snails and urchins).
First, brittlestars/serpentstars are TOTALLY different beasts than seastars. These guys are generally opportunistic and while they will "scavenge" for leftover food I do recommend they be spot fed now and then to assure they will get enough food. This could mean something like shrimp pellets and watching that they get some, or actually handing them a piece of something meaty on a skewer. Few, IMO, are "algae eaters" in the sense that they are "grazing" on algae like snails or urchins. I don't think that is likely.
They are not likely to climb out but I suppose it is possible for them to do it accidentally. The predatory nature of green brittlestars is an individual difference. Not all will be predatory, but they are a known predator. They should NEVER be left to scavenge, but spot feeding may not prevent predation.
Chocolate chip stars are predatory and can be spot fed something meaty. And they should be spot fed. They are not reef safe, and may pose a definite threat to snails, clams, corals, anemones, etc.
Blue Linckia or any other reef safe stars DO NOT EAT ALGAE AND ARE NOT EATING DETRITUS OR WASTE. They are NOT part of a clean up crew as commonly sold. They really must have large amounts of LR in the majority of cases - for a blue Linckia, probably a minimum of 100lbs to start...and that is probably an underesitmate. They feed on encrusting critters, bacterial/microbial films or (more likely, IMO) the microscopic creatures that feed on it...the actual diet is unknown. Few, but some, will take to spot feeding but this should not be relied on. This is true of all "reef safe" stars. Many will die of starvation in 9-12 months if there is insufficient LR. 9-12 months is considered the amount of time it takes a healthy wild caught specimen to starve. IMO, NO judgement should be made on their health until they have been in the system at least a year. They are NOT eating nuissance algae such as hair, slime or whatever...otherwise we would basically ALL be able to keep them and it is clearly not the case.