How can I fight the potential father of this child, when he is claiming to have pictures of my home and pictures of me smoking and drinking?

No. Wait until the child is born and if he then wants to be a father, he or you can file a parentage action.

Clearly you are having difficulty with the potential father, I would suggest you get yourself an attorney. As for DNA test, there is no question you are the mother of the child in your womb but without a sample of his DNA will be impossible to determine paternity unless there is another potential father who will be providing a biological sample and is confirmed to be the actual biological father. Regarding your ability to do these things, as long as you are not violating any law or court order your free to do if you wish. Again, I would highly recommend you counsel with an attorney.

First, stop smoking and drinking. You are pregnant and that is bad for the baby. Second, if he is the father, he has the right to be the father and you can't keep him away from the child (unless he is bad, i.e. drugs, pedophile, etc.). You can have the DNA test done, but if he is the father, get used to him being in yours and your child's life for at least the next 19 years.