No, they can't. When you block a user, Snapchat ensures that they are cut off from seeing your stories. This is part of the privacy features of the app. By blocking, you are essentially saying that you don't want that person to have any form of access to your Snapchat content, and that includes your snap stories which are often a way of sharing your daily moments or thoughts with your friends or followers on the app.
Of course. To unblock someone on Snapchat that you had blocked from your Snap Story, start by opening the Snapchat app. Then, access the settings. Scroll through until you find the list of blocked users. Identify the person you wish to unblock and take the necessary steps to unblock them. However, if you have very restricted privacy settings for your story, they still might not be able to see it even after being unblocked. You may need to review and potentially adjust those settings so that they can have access to your Snap Story again.
To hide a story from someone on Snapchat, you could also create a custom list of friends who can view your stories and exclude the person you want to hide it from. Another option is to set your story to only be visible to your closest friends. It's all about managing those privacy settings to your liking.
Yes, you can screen record Snapchat stories on your device. On an iPhone, you can use the native screen recording feature. Just swipe up to access the control center, tap the screen recording icon, then open Snapchat and play the story you want to record. But note that Snapchat might not like this as it goes against their privacy policy in a way.