Diablo – Do I need to download Diablo II and the expansion seperately from battle.net to play

The LoD expansion expands the original game - it includes everything in it, but adds more content such as new classes and a new act. It does not replace the existing acts, so the answer to your question is yes, you can play all the D2 acts on D2:LoD.

If you have Lord of Destruction there's not much reason for you to run the regular D2 (unless you want to play online with friends that don't own it, if I recall correctly - it's been a while).

The CD key is the key you need. Simply type in the key you already have, and the game should be added to your account. You can also download the game from the website after you've done this.

For Diablo II, I seem to recall it generates a new, longer key, and I think you'll need this longer key for the downloadable version - but as long as you use your CDs, you can just keep using the key you already have.