Yes, now we’re getting somewhere! There was no reason to tag it, because there were no spell types. All spells were just spells. No special distinction between them. A Fireball was just the same as a Shadowform or an Iceblock. It was a spell. Now, however, there are cards that interact with certain types of spells, so those spells got a type. Back then, it wasn’t needed, but now it is. So, what didn’t exist before, exists now, but in Classic, it still doesn’t exist.
Or maybe, the fact they didn’t add a hidden tag was because they didn’t want the Classic cards affecting the quest.
Yes, the fact that it doesn’t say “Fire” at the bottom of the card and the fact that the artwork didn’t change. It’s exactly the same spell, except now it’s a Fire Spell while back then it was just a spell.
Yes, you can, because if you change something retro-active, you only change it in the present, not in the past. And Classic is based on the past.