There could be a variety of reasons. Maybe they miss you and want to know what you're up to. Or it could be a subconscious habit. It's hard to say for sure without knowing more about your specific situation.
It could be that your ex is just randomly browsing and happened to come across your stories. Or, they might still have some lingering feelings and want to keep tabs on what you're up to.
Well, if you think that by letting your ex watch your stories, it could potentially lead to reopening old wounds or causing unnecessary drama, then no. However, if you've reached a point where you're friendly and there's no hidden agenda on either side, you could consider it. For example, if you have mutual friends and the stories are just about general life events that you wouldn't mind them seeing as part of a normal acquaintance, it could be fine. But always be cautious as it can be a slippery slope if there are still unresolved feelings.
Your ex might still watch your stories because they still have some feelings for you or are just curious to see how you're doing. It doesn't necessarily mean they want to get back together; it could just be a habit or a passing interest.