You should put your live site into maintenance first, unless you're confident of not receiving orders during your conversion - though it's best to make sure.
You only need to apply database updates for mods that are not already in your live database.
Yes, pointing the URL to the tested site is my preference too. Most people seem to prefer the idea that the location of a site is fixed and the tested version moves to that location. I've always wondered why they would want to put themselves through the stress of moving a couple of thousand files and often the database too, when there's a tested version nearby that needs only to be pointed to.

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