It makes no difference - you have tax records proving that you were capable of earning X, and now you're claiming that you only earn Y. The court can look at recent earnings (as in the past couple of years), and what you're capable of earning. If you had left to go back to school in order to provide better for the child, the court can decide that your education is intended to benefit your child and therefore is not a case of voluntary underemployment. You have a different problem though - you left your high-paying job before you'd even met Mom.
You can absolutely ask the court to give the child your name, or to hyphenate. There's no guarantee, but it's up to you.
Domestic violence is a non-issue.
Don't forget that you don't have to roll over and give up. If you're going to object though, make sure you're doing it properly and for the right reasons.
You need an attorney, in all honesty.

