Ted Cruz went to Princeton University (AB)Harvard University (JD)
Yes, Ted Cruz speaks Spanish. He is fluent in both English and Spanish, having learned Spanish while growing up in a bilingual household.
If the question is about whether he is eligible, most sources say yes, since he was born to American parents (even if he was born in Canada). If you are asking whether he will be elected, that is doubtful, but certainly anything is possible, as my colleague on this page noted.
If his mother was a U.S. citizen when he was born then he may have been a U.S. citizen from the time of his birth. One does not need to be born in the U.S. to qualify for the U.S. presidency, as long as they have been a U.S. citizen since birth.
The term "amnesty" in US politics, and presumably when 2016 Presidential Candidate Ted Cruz uses it, typically refers to the idea of giving the Illegal Immigrants in the United States some sort of pardon for the crime of illegal border crossing. It can be as minimal as ceasing the deportation proceedings of Illegal Immigrants, but is usually a reference to a "Path to Citizenship", where the Illegal Immigrants will be able to apply to become US citizens under certain conditions set out by law.
No, although some people that are strongly opposed to his views may see him as insane, there has been nothing to point towards it actually being true.