The officer took my license and gave me a 30-day permit. Does that mean I have a suspended license?

Not necessarily.  This is a process known as the "thirty day rule."  The permit you got in place of your license is a report made by the officer to the DMV requesting your license be suspended administratively for a minimum of one year.  You have thirty days from the date of arrest to appeal the report and request an administrative hearing.  If you do not answer within thirty days, your license will be suspended immediately on the forty sixth day after your arrest.  An appeal gives the opportunity for a postponement and can possibly keep a suspension from happening.  The administrative hearing is separate from a criminal hearing and is held at the Office of State Administrative Hearings (OSAH).  The hearing is informal and its purpose is to determine if your license should be suspended, not guilt or innocence for your DUI.