Formula to extract Employee work schedule report from "date of hiring list"

First off - please remove "Need Help with" from your title - it adds no value and detracts from search facility

You can do this with formulae if you want if you're prepared to use some lightweight helper calculations.

First off I should point out initially there are some discrepancies in your sample:

-- B8:B11 should be 09 rather than 10 I think

-- I don't understand why in week 1 you show only one employee rather than two (#1 & #2) - if someone starts on a Monday surely they count in that week (ie #2)

Attached is a basic example of a formula driven approach which reflects the following:

to Data sheet we add the following calculations:

Data!C2:
=$B2+MOD(-WEEKDAY($B2,3),7)
copied down (this gives us a Monday adjusted date)

Data!D2:
=SUM($D1,$A1<>"Service Stopped")
copied down (this gives each Ee a unique incrementing ID number)

With the above in place we can generate the results matrix

On the Report sheet first we insert a new Row 1 (ie blank row above dates) then:

Report!A1
=IF(LOOKUP(A$2,Data!$C$2:$C$11,Data!$A$2:$A$11)="Service Stopped",0,LOOKUP(A$2,Data!$C$2:$D$11))
copied across to R1 (this gives us count of active Ees in that week)

Report!A3
=IF(ROWS(A$3:A3)>A$1,"",LOOKUP(ROWS(A$3:A3),Data!$D$2:$D$11,Data!$A$2:$A$11))
copied across matrix of say A3:R12 (this gives the Ee listings per week)

The above is all possible given the Data sheet info. is sorted by Date Started column.