I thought D2:ED at least did a disk check on install? There was no DRM removal patch for D2:ED, anyway (due to contractual issues), but I guess budget re-releases may have dropped the DRM.
With the original English retail release, the game could introduce problems if it failed to detect the disk in a drive (high level 'rich bandits' early in the game, error code 42 when trying to save, a very large skill point bonus on reaching level 15, etc). The DRM gets chosen by the publisher, though, so different regions can have different implementations.
I would think the game should already be updated with a budget re-release.
Not all retail releases had a serial code. In that case, to get an upgrade to D2:DC you can provide a personalized picture of the back of your box (with the barcode clearly visible) instead.
Compared to D2:ED + FoV, DKS contains a bunch of (mostly small) changes, additions and balancing tweaks to the original game.
D2:DC is pretty much DKS with an optional cheat menu window, added as a bonus for the anthology (see the blog post
Hatching the Anthology).