Formula to return count of duplicate dates based on multiple criteria

In Google Sheets, I have a column of dates in A and checkboxes in column B (Redeemed).

1. I want a formula to count, for each unique date, how many times it appears in the column where the following two conditions are also met:

   1. The date is in the same month as a lookup date in D2
   2. The checkbox in the date's row is TRUE (ticked)

2. I want to use that count to calculate:

   1. In E3, the sum of the count
   2. In E4, the number of times the count includes the number 2
   3. In E5, the number of times it includes the number 3
   4. In E6, the number of times it includes a number >=3

Example Showing Results E3:E6

In the example above,

1. E4=11 because there are 11 dates in the month of October, 2023 (lookup month) that also have their "Redeemed" checkbox ticked.
2. E5=1 because there is only one date, 10/2/2023, that appears exactly twice, is in the lookup month, and has the "Redeemed" checkbox ticked.
3. E6=1, only 10/5/2023 appears exactly 3 times and meets the other conditions
4. E7=2, 10/5/2023 and 10/10/2023 appear 3 or more times and meet the other conditions.