[AT&T, Rogers, Bell, Telus Samsung Galaxy S III] kssxs:
Answers in-line below...

To answer your question in the shortest way possible: flashing.

Here's some further explanation, however, if you're interested ;) :

Rooting your phone voids your warranty. There are many schools of thought on this, and most people agree that manufacturers should allow the OWNER of the device to decide what to do with it. Unfortunately, the manufacturers don't agree with the people ;) . Samsung has implemented a flash counter that increments if you flash a NON-STOCK ROM using the Odin tool. (However, if you flash a non-stock ROM using CWM, then apparently it doesn't increment.) The process of rooting doesn't increment the counter, however, but it DOES change the 'System Status' of the phone to 'Custom' or 'Unofficial'. So if you took your phone in for warranty repair, they would know you messed with it and would probably deny you warranty coverage. The incremented counter also disqualifies you for warranty coverage.

Regardless, if you need a warranty repair and you've rooted your phone, you could always just re-flash, using Odin, an official Samsung ROM, which is freely available to download, and it would return the 'Status' to 'Official', and Samsung wouldn't know any better, and you would have lost your root, since it restores your phone to it's original state (of course you would also wipe Dalvik cache, reset settings, wipe the phone, etc).

Now the flash counter itself... if you flash a non-stock ROM using Odin, it would increment the counter. Even if you flashed back to a stock ROM, that counter would stay incremented. To fix that, another XDA member by the name of ChainFire wrote an app called TriangleAway, that resets the flash counter to 0. You can buy the app from the Play store for a small price to support the author, or download it for free from this link (generously provided by the app author as well):

http://xdaforums.com/showthread.php?t=1494114

Confused yet? :p

Yes, as I explained above, you would just wipe Dalvik cache, reset settings, wipe the phone, and then re-flash a stock ROM using Odin, and you would lose root, and AT&T would be none the wiser. Since you're not planning on flashing any custom ROM's, you won't have to worry about the flash counter being incremented. You can check the status of the flash counter by going into 'Download' mode, and it's shown there.

What causes the loss of IMEI is still an unknown. There are some theories pointing at there being a problem during flashing of custom ROM's that corrupt the IMEI, but nothing conclusive. Some of the latest OTA updates to the phone's modem and OS may have corrected the original reasons for the problem occurring, but Samsung isn't telling us that ;) so we really don't know if it's fixed in newer releases of the phone software. Whatever the deal is, the best and safest bet is to make sure your IMEI information is backed up and kept safe.

Yes. If you flash a stock ROM that has root injected, then you're technically flashing a custom ROM, but since it's the stock ROM, you don't have to worry.

Hope that answers your questions! :p Remember, reading is a good thing!

PS: To anyone else reading this post, if I got anything wrong, please correct me!