If a sea apple happens to die (theyre pretty hardy though), theyre toxic to fish but not inverts i dlnt believe...definitely not corals
(I'll address the thread topic after addressing this, but I will say first that a filter feeding cuke would be a neat pico tank centerpiece.)
Yeah, all sea cucumbers (including sea apples) are toxic - some are just much, much less likely to release that toxin than others, and some contain less of it than others in the first place. As a general rule (there are exceptions), filter-feeding sea cucumbers are more likely to release toxins than deposit-feeding (A.K.A. sand-sifting) cukes are, and they are more likely to contain more of the toxins as well.
The toxin - Holothurin - is an ichthyotoxin (so it primarily impacts fish); importantly, however, like many other toxins, it will affect inverts (and people) in high enough concentrations. In most aquariums this isn't an issue, as most cukes kept contain relatively low levels of the toxin and are kept in tanks with enough water to dilute it, but it could potentially be an issue in a pico tank if toxins are released into the water (so don't touch the water in the pico if the cuke dies - just change 100% of the water and move on at that point to be safe).
Sea cucumbers can release Holothurin in a variety of ways when severely stressed and when dead/decaying (the toxin is literally in the body - the body wall, organs, etc. - so the cuke doesn't need to be alive to produce the toxin). So, keeping sea cucumbers in a low stress environment is key to avoiding the release of toxins - don't keep them with anything that might harass them (thankfully, not many things typically kept in aquariums bother cukes), make sure they can't get harmed by the equipment/setup of the tank (cukes and unprotected powerheads don't get along), watch for signs of stress or poor health, remove them right away if they die, and keep carbon and mixed saltwater on hand in case of emergencies.
All that to say, in most cases, sea cucumbers are cool, beneficial critters in our tanks and don't "cuke nuke" the tanks even if they do release their toxins - the rare cases where they do "nuke" a tank are good reminders to be aware of and prepared for the risk that they might though.
Alright, now for the actual thread question:
For experimenting with a pico, my first thoughts would be:
-Setup an Aquilonastra ("Asterina") tank and run various feeding experiments to determine their specific diet/dietary needs.
-Setup an oddball, mini, predatory invert tank with something like Tanaids or Anthuroidean Isopods and see if I can't figure out how to get them reproducing. Sea Spiders (Pycnogonids) would be a fun option here, but not my personal preference (and coldwater ones are easier to obtain than tropical ones).
-Obtain some Sand Castle Worms (or something similar like Barnacles or Bryozoans) and see if I can get them building a successful colony/reef in the tank.
There are definitely other interesting things that could be done as well, but these are the most experimental ones that come to mind at the moment.
