The leaf shows 1 January 2001. Using odd days, on which day of the week did 1 January 1601 fall?

From 1601 to 2000 is 400 years. Each block of 100 years has 5 odd days, except the one ending in a year divisible by 400 (here 2000), which has 6: $5+5+5+6=21=3\times 7$, i.e. 0 odd days. So 1 January 1601 was the same weekday as 1 January 2001: Monday. (Tuesday treats all four centuries as 5 odd days.)