Or depending on your situation, you could say also the manage of the restaurant.

Yes, but you would not use them in the same way. You would only use the genitive form (possessive 's) in certain situations. If you are focusing on a specific restaurant and the people associated with it you might refer to 'the restaurant's manager' , or 'the restaurant's owner', in the same way as you'd say 'the restaurant's reputation'. If you are talking about a profession or role you would use the compound noun 'restaurant manager' e.g. 'He's training to be a restaurant manager'.

It depends on what you're trying to say. "Restaurant Manager" is a title in and of itself. "Restaurant's manager", is more of a job description. The word "manager" is the title in the job description.

Both are correct, 's = means ownership. So, Restaurant's Manager means that restaurants manger specifically. A Restaurant Manager can be a manger for any restaurant.