The Hadiths indicate that it is permissible for the one who is observing a voluntary fast to break it especially if he is invited to eat by a Muslim.

The time for Witr prayer lasts from after `Isha’ prayer until dawn begins. Once dawn begins, the time for Witr is over, based on the words of the Prophet: “Pray Witr before morning comes.”

All the ways of offering Witr prayer have been mentioned in the Sunnah, but the best way is not to stick to one particular way; rather one should do it one way one time and another way another time, so that one will have done all the Sunnahs. For more about how to pray witr, see the detailed answer.

The adhan and iqamah are only for the obligatory prayers. But for Tarawih, Witr and other optional (nafl) prayers, there is no adhan or iqamah.