Skyrim Add-ons and DLCS
Solution 1:
You have all of the DLC if you have what you listed.
On consoles, mods are handled through the launcher/main menu for the game. If you don't see something that lets you connect to Bethesda's mod service (the only one supported for console), you can't get them. As I recall, Bethesda asserted a lack of mod support for 360 some time before Skyrim Special Edition came out.