What does the stop sign mean?

You have stopped as this sign requires, but parked vehicles block your view along the cross street. What is the correct next move?

Edge forward until you can see, then stop again before you commit

The sign fixes where the legal stop happens, not where the view is. After that stop you may creep to a point where you can actually see along the cross street, and stopping a second time there costs you nothing.

You reach this sign at an intersection that has both a painted stop line and a marked crosswalk in front of it. Where do you stop?

At the stop line, then creep forward only if you still cannot see

The first stop is at the line, because the space between the line and the intersection belongs to people crossing on foot. If you still cannot see once you have stopped there, you creep forward slowly and stop again at the point where the view opens. Stopping past the crosswalk first takes the crossing away from the people using it.

You are second in line at this sign. The car ahead of you stops, then pulls away into a gap. What do you do as you move up?

Make your own complete stop at the line before you go

The sign applies to every vehicle, one at a time, not to the group. Following the car ahead through means you inherit its gap in traffic without ever having looked for one of your own. Stop at the line, look for yourself, then go.

You stop at this sign, and a vehicle is coming along the cross road, which has no sign facing it. What now?

Wait, because stopping does not give you priority over that traffic

A stop sign tells you where to stop, it never gives you priority over the road you are joining. Traffic on the through road keeps its right of way and nobody on it is required to slow for you. Pull out only when the gap is big enough that the other driver does not have to lift off.