Short answers, pulled from the story.
Hathor does not clearly appear until the Fourth Dynasty around 2575 BC. Images of cattle and women with upraised arms resembling bovine horns existed before 3100 BC, but she emerged as a distinct deity during this period.
Her name translates to house of Horus but can also mean my house is the sky. She became a solar deity and feminine counterpart to sun gods such as Horus and Ra while serving as mistress of the sky and mistress of the stars.
Festivals during the inundation incorporated drink music and dance as a way to appease the returning goddess. The Festival of Drunkenness Tekh Festival included drunken revelers playing drums and carrying bouquets of flowers to reach religious ecstasy.
Pharaohs dedicated several temples in Nubia such as those at Faras and Mirgissa. Egyptians maintained trade relations with coastal cities of Syria and Canaan particularly Byblos placing religion in contact with that region.
In Middle Kingdom Coffin Texts and later sources she frequently linked with afterlife. As early as late Old Kingdom women said join worshippers Hathor afterlife just men joined following Osiris, and by Third Intermediate Period around 1070 BC Egyptians began add Hathor's name deceased women place that of Osiris.