Object states on main nav slide not affected by variable change

You are right that variables are global, and their content is available to any slide. That means you can put them in the "If" part of a trigger, and it can complete its function or not depending on the content. The content can control trigger completion, but cannot initiate trigger action. Don't confuse the act of their content changing, which is an action that can initiate trigger action. with the content itself, which can be used to determine if the action should be completed.

Only the slide that changes that content can "hear" the action of changing; no other slide has a listener. In this case there is one slide open, the branched slide that makes the change. The nav slide is not open when the change occurs. By the time it is open, the act of changing is long gone, and it doesn't hear a change to initiate those triggers. Probably the best option is to write the triggers as "Change state of PictureX to State Y when timeline starts on this slide if HowMyschedWorks = true".

The point about the Visited state is that if you create a trigger that says "Change state to Visited", and use the actual name "Visited", there is s high possibility you may have unpredictable problems.

I'm not in a place where I have SL, so I can't comment on the example, but I wanted you to have an answer without having to wait on me.