Also known as Naraka Chaturdashi(the day Narakasura was killed by Lord Krishna) Dhanalaxmi puja is also done on that day; some do instead dhanya laxmi puja;

Kedareshwara vrita was performed by Gauri to obtain the half body of Shiva. When the pramatha gana brangiriti did the pradaxina for Shiva without including Parvati. Shiva explains on enquiry by her that those who know brahman have nothing to obtain from you hence they do not do the circumambulation. Parvati, in a huff of anger leaves the place and enters the forest. Encountering the sage Gautama she asks the sage a way to obtain the half body of Shiva. He asked her to perform Kedareshwar vrita. It starts from ashtami(8th day) and culminates on amavaasya day. In practice however, it is generally done on the last day. So it is the worship of Lord Shiva and the name is Kedareshwara vrita.

All pujas call for some austerities like fast or semi-fast on fruits or milk or juices. There is no exception for this.