Release Update Only to Existing Users?

As far as I know, the only way to allow people to download apps that are in the store but not publicly available is through the use of promo codes. You can generate up to 100 promo codes for each version of an app, so the new version you're talking about would also be subject to that limit. If you were to use this way, you'd only be able to give the update to 100 of your users. So the answer to your question would be no, that you cannot push a private update out to all users.

Is there a reason you need to keep both the old version and the patched version off the air? If the old version had really bad problems, wouldn't they be fixed in the new version? And there's no shame in keeping an outdated version live while you're working on its replacement.

>Is it possible to de-list my app

There is no such thing as "de-list'. You can check "Remove from sale" under 'iTunes Connect / MyApps / Pricing and Availability 'and no one new will be able to buy it. You can then create a new version and submit it for approval. Once it is approved and available for sale check "Remove from sale" again. Current users will be able to upgrade to the new version if they wish even though it is marked "Remove from sale".

If the update is approved, you can raise the price of the old version to significantly higher than the new version. It thus becomes unlikely that the old version will be downloaded by new users. You can also empty the old app's App Store description except for a mention of the new app. iTunes will still notify previous users of the old app of a potential (optional, not pushed) update, and without showing the new higher price.

I'm confused. There is only one app; it can only have one price at a time. Not sure what you mean by putting a price on the "old version" vs. "new version" since only the new(est) version will ever be available for purchase.