Is a father considered an infidel (kafir) or a heretic (zindiq) simply because he is a Sufi who attends mawlids (celebrations of the Prophet's birth), and are his prayers, fasting, and night vigils unacceptable because of this, especially given that he does not engage in other Sufi innovations (bid'ah) like dancing and visiting graves?

The death of your father, as you described it, portends a good end for him. Judging your father to be an infidel merely because he was a Sufi is a great ignorance and injustice. Not everyone who falls into disbelief has disbelief befallen them. Sufis are of different kinds; among them are the good and the bad, and not everyone who affiliates with them is a transgressor or an infidel. A judgment upon someone is based on what they manifest through their actions. These people must repent to Allah Almighty and exercise justice in judging others, distinguishing between the good deeds of a doer of good and their misdeeds. Their statement that praying the regular supererogatory (Sunnah (definition) Ratibah) prayers in the mosque is an innovation is incorrect, because the Prophet (peace be upon him) was proven to have performed them both at home and in the mosque, and it is permissible.