Is it safe to set “open to work” status visible to recruiters on LinkedIn?

I have done that in the past and saw more recruiters reach out to me during that period.

Yes. They hide it from people within your current organization, so it’s unlikely an employer will see it. That said, many people have it on in perpetuity (or forget about it); I wouldn’t give it a second thought.

Yes.

Yes, More recruiters will reach out to you ..Also your manager plans for your replacement at the same time...In some cases if he came to know

The quality of recruiters reaching out seemed to improve a bit. The usual recruiter spam happens regardless of whether you have this turned on or not, but I noticed that people who have actually read my profile and have decent jobs tend to happen with the “open to work” setting on.