Using COUNTIF to count text derived by formula

hi David. the column D in Log sheet is merely formatted as days. keep in mind that formatting cells only gives you a change presentation, not changing what it actually is. what it actually is, is still the Date in column B. so use this formula instead in D2:
=TEXT(B3,"dddd")

or in Weekly Analysis sheet:
=SUMPRODUCT(--(TEXT(Log!$D$3:$D$32,"dddd")="Friday"))

to break it down by morning, afternoon & evening; you need to tell us how you define the 3. say morning is 8 to 12pm. then:
=SUMPRODUCT((TEXT(Log!$D$3:$D$32,"dddd")="Friday")*(MOD(Log!$C$3:$C$32,1)>=8/24)*(MOD(Log!$C$3:$C$32,1)<=12/24))
change the ones in red to the timings you want

Some of your data is incorrect.

Column B has different times to what displayed in column C
In particular
B9 and C9
and down as far as B32 and C32

you have gotten caught by the "formatting of data, is data" error
Start with this in D3 of 'LOG' sheet:

Formula:

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drag down
then this in A2 of 'Weekly Analysis':
=COUNTIF(Log!D3:D32,6)
This will return the information your sample wants
BUT we can get the whole week numbers quite easily
IF you want them in columns, then in A2 'Weekly Analysis' sheet: (with Sunday as day 1 of week)

Formula:

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drag to G2
See Attached (.sol1)
IF you want them in rows, then in A2 'Weekly Analysis' sheet: (with Sunday as day 1 of week)

Formula:

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drag to A8
See attached (.sol2)

Hope this helps