I get mixed information from people about updates. I know that just updating your file doesn't push them, but can it be done from Kindle's end? Can people get an update, like overnight, and when they open their Kindle to continue reading, they notice the updates?
Nope. You can ask Amazon to push through the updated version, but unless it's a major change they generally wont bother. Plus, if people have read it already, they're not going to go back and read it again just because it's been updated.
You should read KDP's policy yourself for specifics, but, basically, if your book was originally a disaster, resulting in a poor reading experience for customers, but now it's fixed, you can ask that changes be pushed to previous purchasers. Only those who have auto-updates enabled will be affected. Tender your request to KDP by clicking the Contact Us button at the bottom of the page.