Extract data between two dates

Assuming your start and end dates are in Sheet1, A2:B2, then in Sheet2, D2 add a helper column with formula:

=IF(AND(A2>=Sheet2!$A$2,A2<=Sheet2!$B$2),COUNT(D$1:D1)+1,"")

copied down. This indexes the matching items.

in E2 enter:

=MAX(D:D)

this gives count of matches.

Now in Sheet1, C2 enter:

=IF(ROWS($A$1:$A1)>Sheet1!$E$2,"",INDEX(Sheet1!A:A,MATCH(ROWS($A$1:$A1),Sheet1!$D:$D)))

copied down as far as you need and across the 3 columns.