counting changed month to month from the same table

Hello emasterd and Welcome to Excel Forum.
Here is an idea for "Evaluate the number of new ID's that have appeared":
1. Add a column to the original data and populate using: =IF(OR(D2<>G$1,COUNTIFS(A$2:A2,A2)>1),"",1)
2. Populate cell G1 using data validation from the list of months in Z2:Z13
3. Populate cell H2 using: =SUM(E2:E16)
If this does what you want then let us know so that we can work on the three other requests.
Note that we may need more information on request number 4, possibly show us how this would be done manually so that we can attempt to automate using formulas/code.
Let us know if you have any questions.