HELP count how many cells are in a specific week number per month

Okay, I made a few minor changes.
First, in Summary!B6, I changed it to Jan 1, 2016 and formatted it as custom mmm (=Jan)
then in B10 and copied to appropriate cells down,
=EDATE(B6, 1) also formatted as mmm

Then in Sheet1!D2 copied down,
=IF(C2<>C1, (B2&C2)*1, D1)
I use this column to find the first and last date (Col A) for each week

Then in Summary!E7 copied across and down (to appropriate cells), this Golliath

=COUNTIFS(April!$B$3:$Z$3,">="&INDEX(Sheet1!$A$2:$A$367, MATCH((MONTH($B6)&COLUMNS($E$22:E$22))*1,Sheet1!$D$2:$D$367,0)), April!$B$3:$Z$3, "<="&INDEX(Sheet1!$A$2:$A$367, MATCH((MONTH($B6)&COLUMNS($E$22:E$22))*1,Sheet1!$D$2:$D$367)))

See attached. Questions?
EDIT: Modified formulas as they would not work for 2 digit months