Highly unlikely- parents don't get sole custody without a reason, the majority of judges won't go for that. In all honesty, he's just saying that to scare you out of doing the test- if DNA tests prove it's his, he'll have to pay child support, and it sounds like he will do anything possible to keep from having responsibility in this- he's not going to go for full custody, he doesn't even want to be named the daddy..
Although provision vary by state, in order to become a criminal defense lawyer you first need to obtain a bachelor's degree. You can choose any major however most people intending to enter law school choose political science, history, criminal justice, or pre-law majors. You must also pass the LSAT (Law School Admissions Test) if applying to an ABA (American Bar Association) approved school. Once accepted you will then need to complete 3 years of legal studies in law school if attending full time and longer if attending only part time. Unlike medical school attending a certain institution does not guarantee you a seat in law school. Students fiercely compete for a seat in a law school. You should keep your undergraduate grade point average as high as possible and strive obtain the highest LSAT score to your ability. I am a pre-law major, so good luck to you future counselor