For as long as you store date/time information as strings, you will have great difficulty using any date/time specific functions and features. If you are getting NULL from MONTH(str_to_date(Created_Date, '%d/%m/%Y')) then the str_to_date isn't converting the strings to dates and the most likely reason for this is the d m y "pattern" is not corrrect.
All you have old us about your "strings that might be dates" is that one of them looks like this: 01/01/2017. Now that could be DD/MM/YYYY or MM/DD/YYYY and we simply cannot tell which one is correct from the single value you have chosen to share with us. Look for any day value greater then 12 in your data e.g. 17/01/2017 ==> DD/MM/YYYY or 01/17/2017 ==> MM/DD/YYYY
Once you have made the choice of which pattern your "strings that might be dates" follow; apply that pattern in the str_to_date() function. You migh want to try a few different patterns to get the best one (and these are just 3 of many you could try):
# which pattern is best for you?
SELECT Created_Date
, str_to_date(`Created_Date`, '%d/%m/%Y') "d/m/y"
, str_to_date(`Created_Date`, '%m/%d/%Y') "m/d/y"
, str_to_date(`Created_Date`, '%Y-%m-%d') "y-m-d"
FROM `CRM_Leads`
You will not have success with your group by query until you choose the most appropriate d m y pattern to apply in teh str_to_date function. Note here that you might also have a variety of patterns in your data, in which case you have an even bigger problem to solve.
Once you have made the choice of which pattern your "strings that might be dates" follow; apply that pattern in the str_to_date() function and ONLY THEN your group by query will work.