Will Fallout 3 and Fallout 3: Game of the Year Edition discs work w/ Xbox One backwards compatibility

Yes.

Will the DLC for backward compatible titles be available too?

Yes. If you own the DLC, you can install and use it just like you do on the Xbox 360. To install DLC you own, go to the Manage Game section for that specific title and install the DLC to your drive.

Will existing game saves on Xbox 360 work on Xbox One?

If you use Cloud Saved Games, your saved game data will be accessible on whichever console you’re playing on.

For more information on backwards compatibility, visit the Xbox One FAQs below

Back Compat FAQ: http://support.xbox.com/en-US/xbox-one/system/compatibility-with-xbox-360-faq

Major Nelson Blog: http://majornelson.com/blog/preparing-for-xbox-one-backward-compatibility-on-the-xbox-one/