risking that I haven’t completely understood what you’re in need for:
My first guess would be that you want to use the count field with a condition. That condition would be a month. In order to get the month, you need to apply the Month() formula on a date field (otherwise with the given Airtable filters currently, you would need a start and an end date). You then apply the count condition (like a CountIF in Excel then) to match only those in a particular month. You could use another condition on the count field for the categories.
Hope that helps!