Why the dates differ
Different traditions hold different days to be his birth. In the north, Chaitra Purnima is kept, and Hanuman is said to have been born at sunrise. In Odisha his birthday is Pana Sankranti, at the start of the solar new year. In the south he is honoured in Margazhi. The day before Diwali is kept by some as the day he was born, and by others as the day Sita blessed him with immortality.
How it is celebrated
Celebrations begin before dawn in Hanuman temples, with the image bathed and covered in sindoor and jasmine oil. Devotees fast, recite the Hanuman Chalisa and the Sundarkand, offer laddoos and jaggery with gram, and give food to the poor. Processions with saffron flags and Hanuman images go through towns. Wrestlers, for whom he is the patron, honour him in their akharas. Rama is worshipped with him, for he is pleased above all by devotion to his Lord.
Hanuman's qualities
Hanuman is worshipped as the ideal servant and devotee (dasya bhakti): strong yet humble, learned yet simple, tireless and fearless in Rama's service. He is one of the seven deathless ones (chiranjivis) and is believed to be present wherever the story of Rama is told, so a seat is kept for him at Ramayana readings. Students pray to him for strength and focus, travellers for safety, and those troubled by Shani or by fear for his protection. On his birthday many recite the Hanuman Chalisa a hundred times, or the whole Sundarkand.