You can always fire your attorney. The problem is that the court may refuse to appoint you another one. Most courts will accommodate a defendant with good reason.
You can absolutely terminate your lawyer. Regardless if the state hired him or not, a defendant can not be forced to accept represenatation. However if you do terminate your lawyer the court is likely to give you two choices 1.) Hire your own lawyer at your expense or 2.) defend the case yourself. Just something to think about before you dump your lawyer
You cannot terminate a court appointed lawyer because you didn't hire him. The Court appoint him. If you are dissatisfied with his service you can speak to him about the reasons or if that doesn't help you can complain to the judge who may or may not remove the attorney from the case.
