Q&A - Pedestrian Controlled Crosswalks

The article Red Means Stop, But Not Always Stay should answer your first question.

For the second, let's look at some law:

Entering through highway

175 (1) If a vehicle that is about to enter a through highway has stopped in compliance with section 186,

(a) the driver of the vehicle must yield the right of way to traffic that has entered the intersection on the through highway or is approaching so closely on it that it constitutes an immediate hazard, and

(b) having yielded, the driver may proceed with caution.

Rights of way between vehicle and pedestrian

179 (1) Subject to section 180, the driver of a vehicle must yield the right of way to a pedestrian where traffic control signals are not in place or not in operation when the pedestrian is crossing the highway in a crosswalk and the pedestrian is on the half of the highway on which the vehicle is travelling, or is approaching so closely from the other half of the highway that he or she is in danger.

When vehicle stopping prohibited

189 (1) Except when necessary to avoid conflict with traffic or to comply with the law or the directions of a peace officer or traffic control device, a person must not stop, stand or park a vehicle as follows:

(c) in an intersection, except as permitted by a sign;

So, if you are at a stop sign, cross traffic is being held up by pedestrian controlled signals and you have yielded to the pedestrian as required, you may proceed with caution. You should not enter the intersection without an expectation of clearing it without having to stop.