Did Pharaoh have a right to ask God why he made him that way?
No, Pharaoh had no right to ask God why He made him that way. He of his own volition rejected God's offer of taking Israel out of Egypt. When God put him on the spot, Pharaoh bristled up and refused to let the people go, hardening his own heart.
Les explains that Paul's argument addresses the objection, 'Thou wilt say then unto me, Why doth he find fault? For who hath resisted his will?' Paul responds, 'Nay, but, O man, who art thou that replyest against God? Shall the thing formed say to him that formed it, Why hast thou made me thus?' Les applies this to Pharaoh: he had no right to ask why God made him what he was, because he of his own volition rejected God's offer of taking Israel out of Egypt. When God put him on the spot, Pharaoh bristled up and said he would not let the people go, thereby hardening his own heart. Though God hardened Pharaoh, it was not that Pharaoh had no choice; he chose to reject God's offer.
Nay but, O man, who art thou that repliest against God? Shall the thing formed say to him that formed it, Why hast thou made me thus?