(A) Even if I have the red light, and the oncoming traffic (from either side) has the green?
Correct. Lengthy explanation to follow:
My driving instructor if I correctly remembered told me that blocking the intersection while under a green, going in one way-direction was not permitted. (I guess not then. . .)
You cannot drive straight through an intersection if you cannot reasonably clear it on the other side in most municipalities, as you indicated here:
The council of a municipality may by by-law prohibit a driver or street car operator approaching, at an intersection, a traffic control signal showing a circular green or green arrow indication from entering the intersection unless traffic in front of him or her is moving in a manner that would reasonably lead him or her to believe he or she can clear the intersection before the signal indication changes to a circular red indication.
But here's subsection (2) of the same part:
(2) A by-law passed under subsection (1) does not apply to a driver or street car operator who enters an intersection for the purpose of turning to the right or left into an intersecting highway and signals his or her intention to make the turn prior to entering the intersection.
(4) Every driver or street car operator approaching a portable lane control signal showing a circular red indication and facing the indication shall stop his or her vehicle or street car and shall not proceed until a circular green indication is shown.
Yes but that only applies if you have not entered the intersection. Section 144 (5) of the Highway Traffic Act:
Where to stop – intersection
(5) A driver who is directed by a traffic control signal erected at an intersection to stop his or her vehicle shall stop,
(a) at the sign or roadway marking indicating where the stop is to be made;
(b) if there is no sign or marking, immediately before entering the nearest crosswalk; or
(c) if there is no sign, marking or crosswalk, immediately before entering the intersection.
If you are already past there, you are expected to proceed and clear the intersection when safely able. A red light does not mean "stop where you are," it means "do not enter the intersection." Think about that. If you are 300 metres back from a traffic light, and it turns red, do you stop right there or drive up to the stop line and stop? Same logic applies. If you are past those points, you obviously can't stop at them so you have to go forward.
However, if the car to the left did collide at me in the rear while I was clearing the intersection under such circumstances (A), would I be at fault?
No. If you entered the intersection on green, you did obey the traffic light according to the rules of the road. As far as your mother's options:
Practically, my mother told me that I would have no choice but to
(i) During the green light, proceed slightly forward behind the blocking car, and turn after it clears
If you are stuck in the intersection on a red light, you do have to clear it ASAP. An exception is provided for people turning left or right, in that you can be momentarily stuck there, but you still have to try to get out of the way. You can't just wait in the middle of an intersection on a red light. Try driving in downtown Toronto during rush hour. If everyone had to wait for a green just to move out of the intersection, the entire city would stop moving.
(ii) Back up
That is a really bad idea. First of all, you will probably still be marooned in the intersection because the person behind you has now pulled up to the stop line, AND on top of that if you back up and hit the guy, you'll be likely charged with Careless Driving AND be 100% at fault.
(iii) Stay in the intersection and slightly block the flow of the traffic until a green passes to turn
If you have an opportunity to clear the intersection, you must. Again, a red light does not mean "stop right there" it means "do not enter the intersection." It does not make sense to strand drivers in an intersection where they are blocking traffic.
(i) Police wouldn't care about anything else except if i had the right-of-way or not - given RED or GREEN signals
Respectfully, your mother's understanding of right-of-way is not correct. You were already in the intersection and therefore had right-of-way.
(ii) It was my fault for proceeding and clearing, seeing that the car to the left is going pass me despite me being in the intersection
No, you did the right thing. He has an obligation to give way to vehicles already in the intersection - even if he has a green light. That's what the "yielding to traffic" provision you posted above is all about. You entered on a green light, therefore you were lawfully using the intersection.