Regarding the day beginning at sundown, here is an explanation from the book Settings Of Silver: An Introduction to Judaism
, by Stephen M. Wylen, which I found at Google Books
"In a solar calendar the new day begins at the morning, with the appearance of the sun. Midnight, the start of the day in the Gregorian calendar, is the earliest moment in the morning. In a lunar calendar the new day begins in the evening. The Jewish day begins at sunset, defined as that time when at least three stars can be seen with one glance at the sky. A Jewish day goes from one sunset to the next. So, for instance, the Sabbath begins at sundown on Friday and ends at sundown on Saturday. In the Jewish calendar Saturday night is the beginning of the first day of the next week."
Regarding the 3 days part, the term that might help in locating an explanation is "inclusive reckoning". If you do a Google search for that term, you'll get lots of pages to look at.