We'll need more detail for a thorough answer, but to get started with.
Create a filter that searches for the issues you want (e.g. "unresolved and due date in the next 7 days"), save it, and subscribe to it. It will email you regularly with the list.
Ok, you'll need some form of escalation script for this. Most of the approaches use the same filter idea I gave you above, but with escalation, you should transition or comment on the issue (both of those can fire an event you can use in the notification scheme and send to "assignee")
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