I am a first-time offender, soon to be of probation. I am also an honorably discharged disabled veteran with a steady source of VA income. Would I be allowed to live in the Philippines and marry my long time girlfriend?

You need to contact the Philippine embassy and ask them. And you need to contact the VA to ensure that once you are no longer in this country you can continue to receive your VA benefits as well. You should go to the VA in person and speak to a supervisor about this.