Legally we must completely stop with the front of the vehicle behind the white line.
One of the reasons is pedestrians. Since every intersection is a legal crosswalk, drivers must stop completely and look both ways for pedestrians who may be about to cross. If there are pedestrians, stay stopped and wait patiently for them to cross.
Another reason is to completely observe that the intersection is safe before moving forward into it. There may be vehicles about to turn from the thru street. There may be cyclists. There may be a left-turning vehicle cutting the corner. There may be a large vehicle about to do a wide turn. There may be emergency vehicles approaching.
After you’ve stopped and made sure it is safe, you can proceed whenever there are no cars or other road users on the thru street. If visibility is blocked due to shrubs or parked vehicles, you can slowly (snail pace) roll forward into the intersection in order to obtain a better view. Prepare to stop again if you see vehicles & road users on the thru street. You can roll up to the edge of the parked cars if necessary. Make sure you look left first, as the car on your left is much closer to you than the car on your right.
If there is a vehicle facing you that wants to turn left, which one should go first?
Normally whichever vehicle stopped and then entered the intersection first, should go first. If you entered the intersection at about the same time, the car turning left should yield to the car going straight. However, make eye contact with the driver and remember both need to yield to vehicles on the thru street. Use courtesy if unsure.