Referring to the book of "Marriage to Parenthood", it states regarding the conception of a child, under the section of what are the makruh times, regarding the time of the month.
It states that it is makruh during the 1st of the Month (except 1st night of Mahe Ramadhan), middle of the month (full moon) and end of the month (when there is no moon).

If you could kindly help to clarify, which dates exactly are middle of the month (when there is full moon)? Does it refer to 13th, 14th and 15th of the Month? Or only 15th?
And end of the month (when there is no moon), would be 29th / 30th?

14th and 15th, as some months are 29 days.
End of the month is when the moon gets into wane stage.