Looking for a formula that is dependent on criteria from a drop down

In D1:
=TEXT(D2,"dddd")

In D2:
=IF(DATE($A$2,MONTH(1&$A$1),1+(COLUMNS($D:D)-1)/2)>EOMONTH(DATE($A$2,MONTH(1&$A$1),1),0),"",DATE($A$2,MONTH(1&$A$1),1+(COLUMNS($D:D)-1)/2))

This will return blanks for short months, instead of running into the next month.