Hello i faced with such a problem, why impossible mermaids saved to SimBin? and shared?

Unfortunately it is part of the code that mermaids cannot be saved to the bin. I'm not sure if someone has created anything to fix it, or if that's even possible. :/

They can't be saved to the bin but you can save them to the library as a household and then share them if that helps.

I can save they through nraas master controller, nraas integration. Why they can not be saved the default?

Good old EA and it's stupid issues. Just like not being able to create or edit aliens in CAS due to some issues (or as they call it for plastic surgeries at the hospital "cultural difference"), even though you can do it with Nraas MC

Actually, there might be an explanation why Mermaids, Aliens and the grim reaper can't be saved the right way in CAS. The grim reaper is a NPC, assigned to do things in the world. Which means this specific NPC is also scripted with the certain animations and (if I recall right), effects. Same for Aliens. I think everything that can't be chosen since the supernatural patch is considered a NPC and won't be saved correctly because then, the game will see it as a regular sim.