Is there a way to find out how many registered users logged in a given time period?
You could count all User table rows in the database where the fields for "Last Access" and or "Last Login" are newer than one month old .  You'd need to compare those timestamps to a timestamp for the start of the current month. You can find that with something like this or maybe it's as simple as:

$this_month_start = strtotime("-1 month");