Ask the user for the first day of the week or calculate it

1. How do you calculate the first week of the month?
2. Is the first week of a month the first full week?

How do you calculate the first week of the month?

First week starts when all days of the given month fall in that week: July 1st is part of June and not part of this month. July Week 1 from 7/2 to 7/8. July Week 2 from 7/9 to 7/15.

Is the first week of a month the first full week?

The first week of the month is the seven days starting with the first day of the month. Hence, in your example, the first week would be Tuesday, the 1st through Monday, the 7th. This way, the first through 4th weeks would always be fully contained within the month, and only the 5th week would cross over.