Can open science project be performed/published by non-scientists? In other words, can anybody publish an open science project, or does the author need to have some specific title or at least study the subject in order to receive some positive feedback from the community?

Or is it simply evaluated based on the quality of the published data and its positive feedback/output?
Yes, of course anyone can publish an open science project. As many of us in the scientific community wish would happen, the project should be judged on merit, not who initiated it, where they studied, or what their background or education is.

These principles are enshrined in the San Francisco Declaration on Research Assessment (DORA), which have been widely circulated and many (unfortunately not a majority, yet) organisations quick to sign up to.