Don't overthink it. It was an accident. Just carry on with your day as normal. If seeing their story made you feel something, try to distract yourself with other activities like reading a book or going for a walk.
It depends. If you still have feelings for them and think there's a chance to reconcile, you could reach out casually. But if it ended badly, it's probably best not to.
It could mean that your ex is still curious about your life. Maybe they still have some feelings for you, or they just can't help but be nosy about what you're up to now.
You should stop right away and apologize. Acknowledge that you invaded her privacy even if it was unintentional. Have an open and honest conversation with her. Listen to her thoughts and feelings without interrupting. Assure her that you will take steps to prevent any such accidental invasions in the future, like being more careful with shared devices or files.
One way is to limit your access to that platform so you don't accidentally see it again. Also, talk to someone you trust about your feelings, which can relieve some of the stress. Over time, as you focus on other aspects of your life, it will fade from your memory.
Personally, I would hold off on reaching out right away. Just because they unblocked you and watched your story doesn't necessarily mean they want to re - establish a connection. It could be a momentary lapse of curiosity. If you do decide to reach out, make sure you're doing it for the right reasons, like if you truly miss them and think there's a possibility of a healthy relationship. But first, give it some time. See if they make any further moves. Maybe they'll send you a message first, which would be a stronger indication that they're interested in talking.