It is better that she would process her entry to Canada outside the Philippines. The requirements are the same anyway. The only difference is that in other countries, the volume of applicants is quite low so the processing is faster than in the Philippines. Of course, she has to secure all the...
I should suggest that you personally visit and inquire the government office (LTO in the Philippines) responsible for processing driver's license in Alberta. A government office can personally evaluate your case and show you the right way. Good luck!
You can study without a study permit in non-formal schools. If you enter a university or college, you will be required with a student visa. If you just study cooking or dancing or acting, then you can do so without getting a permit.
She really has to complete the number of required college course credits. There is no shortcut. It doesn't matter where she will get the courses. There are many cheap colleges in the Philippines that she can enroll even for a semester, granting she enrolls full-load.
You will never go wrong with an accurate fact. Correct it as soon as you can. It will save you a lot of trouble in the future. Don't wait for the authorities to discover the discrepancy later. That's too risky and may jeopardize your PR application.
Just give it a try. There is no harm in trying. The web is a big help but writing personally to a prospective employer will make a lot of difference. I don't think the embassy can help you much. It is not the function of embassies to provide jobs.
Same in the US. If you do not have an established job or business in your homecountry, you are not likely granted a temporary work permit. Before you reapply, you should improve first your status, otherwise reapplying might just waste your time.