If the police didn't read me my Miranda rights, have my DOB wrong, and a DV is my first offense besides a couple speeding tickets, can I get away from all the charges if she decides to drop or what is there that I can do?

Nope.

The other partner can not "drop" charges, in fact most states have laws that require her to testify even if she does not want to.

Date of Birth is a minor issue and not part of the formal charges, the officer will formally ID you in court.

You are watching way too much TV, police do not read you your rights when you are arrested, that is just TV shows. They may read you your rights before they question you. If they don't what you said can not be used against YOU. If you were taken to the station and questioned there, that is where normally your rights would have been read there.

So sorry none of this will cause the case to be dismissed.

Lawyer and good plea deal or fight in court