Is that ok to say
go right meaning turn right? Or I have to say only
go to the right?
"Go right at the traffic lights" is entirely idiomatic, meaning turn right. "Go to the right" sounds unusual to me as a native British English speaker.
"Move to the right" is common. In terms of driving it could mean change lanes+, in other situations it could just mean you're in my way, there's space to the right, move into it.
+My thanks to David Garner