1. Usage out of combat or when there's nobody around
Q: Could this be used out of combat?
Yes. All powers can be used out of combat. The power reacts to the trigger "You become bloodied or brought to 0 or fewer hit points", and that includes, say, falling off a cliff or damage from a disease.
Q: There are no applicable targets
Then nobody gets Hit and you don't get any of that extra 1d6 healing. However, the Effect says you can spend a healing surge, so you may do so.
Q: you can't take immediate actions on your turn – and out of combat, you can't exactly be on or not on your own turn.
That doesn't really matter. If there's no combat, there aren't turns, so it's not your turn either! But really, outside of combat, you should be able to trigger this, unless you could imagine the thing that hurts you as something that would occur on your turn (e.g.: you fall onto spikes, or stab yourself in the gut).
2. Vaporization and other Oh Nos!
Q: Let's say the triggering health loss is so severe that it kills the Swordmage outright. Let's say they're vaporized into dust. Can they interrupt and use this?
Immediate Interrupts occur at any point during the trigger, before it is completely resolved. They're defined in the Rules Compendium as such (and are distinct from Reactions, which occur only after the trigger has completely resolved):
Interrupts: An immediate interrupt jumps in when its trigger occurs, taking place before the trigger finishes. If an interrupt invalidates a triggering action, the triggering action is lost.
Mechanically, your Swordmage heals just before taking the damage. Things then get pretty simple: either they heal to a point the damage won't kill them, or they don't, and the damage kills them.
If your Swordmage is already at full health and is about to take enough damage to kill them outright, this power can't help you - you won't be able to heal further unless some other feature allows you to. Your character will be killed outright. You may then complain to your DM.
Side note: This power's necrotic burst might save your life.
Suppose you're being reduced below 0 hp as the result of someone using an attack power against you. If the attacker is caught in your necrotic burst, they might get knocked out by the damage. You might also have a power or feat which can render them incapable of performing their attack! If you do knock out your attacker during the burst or render them incapable of attacking you, you're invalidated their action and that action is lost. They've lost their standard action (or what have you), and their attack un-happens. You'll heal and be safe.
3. How do you heal?
Q: If the answer to #2 is yes, do they start at 0 hit points (effectively negating all damage they would have taken beyond that point) and heal from there as they would when healing under a "dying" condition normally?
If your character were to be healed whilst dying (e.g. using this power), then Healing the Dying (Player's Handbook p295, Rules Compendium p261) says you'd be restored to 0hp and then healed.
However, let's consider the three possible scenarios here.
- Your character's HP is positive, and brought below 0hp, and this power is triggered: You heal as normal. You're not below 0hp when the healing occurs, so the Healing the Dying rules don't apply.
- Your character's HP is negative, and brought lower: You're unconscious. You can't take actions and cannot trigger this power.
- Your character's HP is negative, a feature is allowing them to remain conscious, and their HP is brought lower: I believe you can trigger this power in this circumstances, since you're brought to a HP value fewer than 0! You would be restored to 0hp and then heal.