If the state requests that a subpoena be issued, there is usually paperwork in the court file that reflects the request, and or a document showing that the witness was served with the subpoena.
Generally speaking yes. Normally an application for a subpoena is issued by the court and placed in the court's file (which the defense attorney has access to). The defense attorney can also file a motion for the state to tell the defense attorney all their witnesses.
The answer is "yes" but sometimes the State and/or clerk do not get the information into the file in a timely manner and it can conceal the State's witness information. It all depends upon the efficency of the clerk's office in most cases.