I'm a total newbie to remixing and producing. What justifies a proper remix? Does this mean that the track has to be completely re-written? The reason I'm asking is because I finally learned how to edit tracks in ableton and I have some really neat ideas about remixing some tunes.

In my view, as soon as you put a new sound into a track it's a remix. If you're just reworking the structure of an existing track then it's an edit.

So it doesn't technically take much for something to qualify as a remix. Although generally, most or all of the original sounds are changed, the song structure and arrangement are designed from the ground up, melodic elements are added in or removed and very often the main melodic theme has it's notes/ structure changed. Some remixes are completely unrecognisable and bear zero resemblance to the original track. Even if you know it's a remix and you listen to both tracks and compare them, you can't find a single thing in common. But that's the other extreme (and it happens very rarely)!