We see further evidence that
Ser Robert Strong
is the Mountain from very early on in the series during one of Bran's dreams:
He saw his father pleading with the king, his face etched with grief. He saw Sansa crying herself to sleep at night, and he saw Arya watching in silence and holding her secrets hard in her heart. There were shadows all around them. One shadow was as dark as ash, with the terrible face of a hound. Another was armoured like the sun, golden and beautiful. Over them both loomed a giant in armour made of stone, but when he opened his visor, there was nothing inside but darkness and thick black blood.
The shadow with the face of a hound is clearly a reference to Sandor Clegane, the hound. It seems likely then that the giant here is Gregor. The stone armour is a reference to his nickname, the Mountain. The fact that his visor is empty foreshadows Gregor having his head cut off and sent to Dorne. Oberyn's poisons also caused Gregor's blood to turn black and thick.
It seems to me like the connections between the Mountain and this knight with an empty visor indicate that the Mountain is Ser Robert Strong. This also answers your second question, since it means that Ser Robert Strong has no head at all. I believe many of the character's mention that they never see him take off his helmet, or do other things such as use the privy, which kind of indicates that he isn't quite human.