As a Greek citizen, you are visa exempt to visit Canada. As you enter, unless somebody tells you otherwise, you will be allowed to stay for up to 6 months. As a visitor, you may not work or study and you are not covered by health care. This is why you should have travel insurance in case you have an emergency.
As for taking your son with you, as has already been mentioned, if you have shared custody with his father you will need his permission. If you take a child from a shared custody arrangement, the father can contact the police in Greece who will contact the police in Canada and have them send the boy back to Greece.
As a visitor, you have no right to enroll your son in school. I have heard about people being allowed to do it and I have heard about people being refused.
If you want to change your status from visitor to worker, you need to find an employer who wants to hire you. This employer needs to apply for a labour market opinion proving that he has advertised the job and is offering market wage and still can find no Canadian who wants it or is qualified. If he gets the LMO, you can take the LMO, go to the border with $150, skip over to the US and on your entry back to Canada, you apply for your work permit with your LMO and get it instantly. You can only start working after you get the work permit. Getting the LMO can easily take a couple of months.
As a worker, you would be able to get health care. However, in order for your son to be allowed to stay with you and go to school, your work permit would have to be skilled. That is skill level 0, A or B.
If you are still in Canada and your visitor status is expiring (6 months almost up) and no work permit in sight, you either need to leave or you apply to extend it showing that you have the money to stay and that you have travel insurance for you and your son.