- You are incorrect in your assertion that a "calendar month" refers specifically to a month as it begins and ends on the calendar. There are, in fact, two definitions of "calendar month":
countable noun A calendar month is one of the twelve months of the year. Winners will be selected at the end of each calendar month.
countable noun A calendar month is the period from a particular date in one month to the same date in the next month, for example from April 4th to May 4th.
The second definition is widely used in employment contracts to specify the length of notice required.
Is there a phrase which denotes a month which is simply any period of thirty days? - No. There is no way to accurately describe 30 days except to say "30 days". You can use "about a month", but this is not accurate.
- I've never heard of a "calendar week" before, but a quick bit of research shows agreement with your general concept of it starting and ending on specific days of the week. For example www.calendar-week.org states:
In Europe the calendar week is a week that begins with Monday and ends with Sunday.
It does seem that "calendar week" doesn't have an equivalent of the second definition that "calendar month" has.
Is there another phrase which denotes a week as any seven-day long period? - Yes. We call this a "week". Unfortunately this is not a precise term, as it can be interpreted in other ways too, e.g. a calendar week, or a period of approximately seven days. Collins dictionary has a good list of the possible meanings of this phrase.
But don't worry, we do have a way in English to specify an exact seven day period that might start on any day: it's "seven days".