- The brief description talks about being knocked unconscious. If a blow would kill you outright, can you still use Reactive Healing?
The initial, italicized description is exactly that: description. It isn’t meant to dictate how the feat is used every time it is used, it’s just there to illustrate a usage. Formal rules and requirements are found in the un-italicized rules text below it.
That text says,
When the damage from an attack or an effect would
Nowhere in the rules really gets into details on the timing of most triggered events like this, but most of them tend to interrupt their trigger. Attacks of opportunity and readied actions, for examples, explicitly do so, in what are probably the only cases that do get into the details. And the English word choices here—“when X would, then Y”—strongly implies that X hasn’t happened yet when Y occurs.
So the healing comes before the damage is applied. If it is larger than the damage dealt, it can indeed prevent you from going unconscious. It can also prevent your death, which is somewhat more important.
- If the healing isn't enough to make you conscious, are you automatically stabilized because you've been healed, or are you still bleeding?
The healing occurs before the damage, so you are reduced to a dying state after the healing occurs, and therefore have not experienced any magical healing while dying. Therefore you are not automatically stabilized.