=WEEKDAY(date, [return_type]) gives the day of the week as a number. The default counts Sunday as 1 and Saturday as 7; with return_type 2, Monday is 1 and Sunday is 7, which makes "is it a weekend?" a simple test: =WEEKDAY(B2,2)>5.
=WEEKNUM(date, [return_type]) gives the week of the year. For ISO weeks, used in Europe and many planning tools, use ISOWEEKNUM instead.
For the day's name, format the date as text: =TEXT(B2,"dddd") shows Monday, "ddd" shows Mon. The result is text, good for labels and grouping.