Deauthorization: what happens?

What happens to my iTunes account and my active authorization on my current laptop?

Nothing.

What are the steps involved in reauthorizing my current laptop once I've done the once-a-year purge of all the deauthorizations?

None.

What problems shall I expect and have other people experienced?

Unless you have an Apple TV, just continue as you have been after the Deauthorize All. It resets the authorization count on the iTunes servers and doesn't actually deauthorize the computers; therefore, you can exceed the normal authorization limit by using it, which is why it's limited to one use per account per year.

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So I don't have to REauthorize my current laptop in order to access my account?

No, you don't. From the perspective of iTunes on the laptop, it was never deauthorized; the change made by Deauthorize All is only on the iTunes server.

What happens to my iPhone link to my iTunes account?

Nothing.

I ought to be able to open My Account, see the list of authorized computers and uncheck the ones I want deauthorized (and then they go away).

An authorized device other than the Apple TV doesn't need to be connected to the Internet to retain its authorization, and if the device isn't connected to the Internet, asleep, or shut down, it can't receive a deauthorization signal from the iTunes Store. Furthermore, some firewalls may block the message, making that functionality impossible to implement.

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