Is Rock Lee guy's son?
No, they are not blood-related. When Lee wasn't in Guy-sensei's team yet, he was often mocked and bullied because of his inability to use any techniques other than Taijutsu. Guy-sensei was the first one to really believe in Lee's abilities, and thus he became Lee'sidol.
Why is Lee's son named metal?
Metal Lee's name is
derived from the metal musical genre and is a play on Bruce Lee, whose given name is pronounced the same as blues in Japanese. It is a continuation of the pun established with his father, Rock Lee.