calendar dates and days of the week.

One way:

All dates and days of 1 month in a single-cell formula:

Please enter in A1 the first day of the month and empty all expected results and try in B3:

Formula:

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Format column B as a date and custom format column C: dddd

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In A1, type the first day of the month, empty all expected results in Column B and C (if there) and in B3, type (or copy) the specified formula.
Format column B as a date and custom format column C: dddd.
See attached file of Post #2.

If this does not work in your own workbook, please upload that workbook here.