Does every singer know how to read music and staff?

Any professional singer can do it. That's called a musician. A singer who doesn't even know the most basic music score, or can't even play a musical instrument, is not worthy to be called a singer.

Professionals have a strong music theory, which is also the basic condition for making good music.

If you insist, it should be the simplest notation for ordinary music players, and you should read it all. The staff is even worse.

Many bands have lead singers who write their own songs, and guitarists who play solo. The arrangement and production are all done by myself. All you need is knowledge of music theory. They don't even know the music score, so they are not worthy to be musicians. This is the most basic!

Therefore, every singer must be able to read the staff and notation and be familiar with music theory. The music created in this way has a soul, not an empty shell.