I would recommend emailing the Student Financial Aid and Scholarships office at [email protected]
for clarification, but as I understand it, if you submit your OSAP application ASAP and receive any amount of funding, you should be approved for McWork.
No, you cannot hold a McWork position if you do not qualify for OSAP, so get in your documentation.
I imagine you would be able to start in the fall, as that seems like the "most recent" fall/winter session.
Email OSAP though; they respond fairly quickly and are always incredibly helpful. They can also give you a certain answer.