I got a part time job, but my program starts from september 6th. For next two weeks can I work or it's illegal to work ?

It already says in the CIC portal you can not, The deal here is you have to be a full time student in order to work full-time/part-time. You are yet to start the course. Hence you can't work until you start your course.

What about spouse of the students who got their SOWP Along with the student's study permit? Can they start work before the study program starts?

Palanivel ChockalingamYes , as you are coming on Work permit, you can start working anytime