I think "He needs to sleep." would be better translated as " Er muss schlafen." (müssen=need/have to)
"He needs his sleep.", "I need my sleep." is a common expression, at least in the U.S., meaning that without (enough) sleep one does not do well. Not necessarily that one needs to sleep right now.
Also in: "Er braucht seinen Schlaf." der Schlaf " is a noun; " schlafen" is the verb. And in this instance it can be translated pretty literally, at least into the U.S. expression. :)