A week free of no school / no work / something else. It is just short for "A week off... from doing what I normally would do". If I have no work next week, I will say, "A week off from work"

It means a week that you do not have work and/or school. If you see it on a timesheet, then it means no work during that week. If it's in regards to school, such as spring break being a week off, it means you don't have to attend classes.

a week to do absolutely nothing.

It can also mean a holiday. Example: I am taking a week off work/school to go on a holiday.

"To be off" is an expression meaning to not have work or class: "I'm off work today" or "It's my day off" = I don't have work this day "I have the whole week off" - this whole week, I don't have to go to work/school. etc "To be off work" is probably the way to think of the full verb - we just drop the word 'work' ... "I'm off today" means "I'm off work today"