I would need more information on the details of this "survivor's benefit" before I can give a full answer. It may be non marital if this was a benefit that accrued before the marriage. Consult with a local family law attorney.
You have a very good chance at getting unsupervised time with your child, as long as you are abiding by your probation conditions and can show you are drug free. You should file a paternity action ASAP.
This is a third degree felony punishable by up to five years in prison. I agree with the previous answer that a prison sentence is highly unlikely, but you need an experienced local criminal defense attorney to make sure your case is handled correctly. It's also a good idea to refrain from talking about the facts of your case any further, except with your attorney.
I agree with my colleagues. If he continues to be unreasonable, file a Motion with the Court. Parents are supposed to be flexible when it comes to parenting time. The judge would not be happy with him, and may even order him to pay your attorney fees. Contact a local family law attorney for a consultation.
Sounds like a good case, based on what you are saying. You should schedule a consultation with a local attorney as soon as possible. If you are thinking about representing yourself because you feel you have a good case, don't do it. A conviction for battery can result in a loss of liberty. If you had a very curable form of cancer, you would still go to a doctor.