I bought the ES anthology and have now tried installing Morrowind through Steam. Yet it doesn't ask for the disc containing Tribunal and Bloodmoon and also I don't know if it includes the other little expansions like 'entertainers' and 'adamantium armour'? How would I find out? The official site has zip files for those expansions but not much help in where to put the files and I can't really see so far how to check on what's installed.

From what I understand, the Anthology comes with all expansions for all the games as well as the base games. Have you checked to see if there are Tribunal and Bloodmoon discs? I just watched an unboxing and the expansions are located immediately after Morrowind itself.

The Steam code unlocks regular GOTY edition which includes Tribunal and Bloodmoon, but not the smaller add-ons. You should see the expansions in the launcher -> Data Files (or just in your Steam folder). Add-ons are installed by dropping the .esp and whatever other files they have in Steam\steamapps\common\Morrowind\Data Files. Then tick them in the launcher to activate them.

Physical copies of Morrowind do not require Steam.

There is no Steam code for Morrowind (or the two expansions) in the Anthology.

The Anthology version of Morrowind has nothing to do with Steam.

Install Morrowind from the main disc.

Install Tribunal from the Tribunal disc.

Install Bloodmoon from the Bloodmoon disc.

(the Construction Set disc doesn't need to be installed, as the CS gets installed when you install the game. This CS disc just has all the BSA files on it. Useful for making mods.)

The eight official plug-ins can be downloaded from a few places. (like, http://www.uesp.net/wiki/Morrowind:Official_Add-Ons)
They are not included with the actual game.

The plug-ins are installed exactly how mods are installed. To learn how to install, go http://www.gamesas.com/topic/106063-morrowind-mods-faq/#entry1772641. To learn all about mods and how to find/use them, go http://www.gamesas.com/topic/1305729-mod-recommendations-for-new-players/.