That are some serious specific questions! Let me respond with my thoughts (for what they're worth ).
You are right to say that, as for our 'main Legacy server' spawnkill isn't allowed as such (like right after losing spawn protection you start shooting them while they are still in spawn isn't allowed). On the other hand: if the enemy (in your example Axis) starts shooting at you while that specific enemy is still in his/her spawn (or even start shooting with his/her spawn protection active, which will be deactivated as soon as they start shooting at you) you are allowed to shoot back! So if an enemy starts shooting at you while you are running through their spawn, you may shoot back even though the enemy is in her/his spawn .
As for players "seeking safe haven in spawn to heal themselves": in my opinion that's not spawnkilling, since the player has already moved out of spawn to fight and then goes back. Even if the player went out of spawn and didn't fight (but got hit by mortar or artillery or something) and then goes back into spawn to heal himself/herself, my opinion still stands that by killing this player within the spawnarea isn't spawnkilling (because he went out of spawn already).
The other question you asked is more difficult to answer, because if you just see someone healing in spawn, not knowing where (s)he came from... you don't actually know if (s)he's been in a fight and is "looking for safe haven in spawn to heal himself/herself" or if (s)he just spawned and gives himself/herself the one package needed to have 156HP...
Thus, to summarize my opinion: if an enemy went out of spawn to fight (or got hit by mortar/artillery or whatsoever) and goes back into spawn to "seek safe haven to heal himself/herself" and you go right after him/her and kill him/her within spawnarea, that's no spawnkilling in my opinion. The other possibility you suggest: you can't possible tell that someone is healing from battle/mortar/artillery or just giving himself/herself the last package to get 156HP... so that COULD be spawnkilling (if the particular player hasn't been out of spawn yet). To conclude: if an enemy starts shooting at you from within his/her spawn, then you are allowed to shoot back at this particular player.
Oh and yes, this seem to be a small book as well . Really curious about what other muppets think by the way, since I'm not the one with all the knowledge here. Just gave my two cents for what's it worth .
Edit: after reading Matu his post I would like to add/clarify that it would qualify as spawnkilling if you kill an enemy that indeed DIDN'T move out of his/her spawn and DIDN'T shoot at you.