Surprise requires a DM's judgement:
Surprising Foes. If the adventurers eneounter a
hostile ereature or group, the DM determines whether
the adventurers or their foes might be surprised when
combat erupts. (PHB 183)
The DM determines who might be surprised. If
neither side tries to be stealthy, they automatically notice
each other. (PHB 189)
One thing to notice about these is that they both indicate the surprised party entering combat, and Jeremy Crawford indicated in tweets that surprise only happens when entering combat (looking for tweet). This matches with the order of combat on PHB 189.
- Determine surprise.
If attacking a sleeping creature at the start of the fight, yes. But, I don't know if RAW allows this to be surprise if the target was previously in the fray and became unconscious by reaching 0 HP...
I'd wager to guess the auto-fail on the save "wouldn't be fair." That said, if they are at 0 HP, as a rogue you should be able to make them fail at least three saves pretty easily -- You attack with advantage b/c they are unconscious, that is two saves, and you get sneak attack which is arguably another lost save as another source of damage (see the question about poison counting as a death save or not) or use a second attack that turn for the last save... And with the auto-critical, you'll likely surpass their max HP to boot. So, in that case I'm not sure if it really matters.