How can the cop's search my car without a warrant?
Since a car is mobile, the law permits a search without a warrant, as long as the officer can state in court, not to you, facts which support the probable cause standard that a crime was committed.
Can DNA evidence change from one person's DNA to another?
No, DNA evidence is tested and a DNA pattern is identified, no matter what happens to the evidence, it cannot become a different pattern.
Why was I not Mirandized, but I was arrested?
Miranda warnings are only required during custodial interrogations. You were in custody because you were arrested, but you were not interrogated, which means questioned about the crime. This is why you were not mirandized.