Combat Clarification
1. I have always assumed that ancillary healing and damage effects could only be played on the current player's "turn," so I'd say the healing was not allowed in this case.
1a. Likewise.
2. Only the Metalworking ability counts towards the played unit's attack (and it ends as soon as damage is resolved). Mathematics and Ballistics are not related to any given units: they're just ways to deal damage around the battlefield.
2a. It is part of he unit's strength as I stated above, but it only lasts for the round that the unit is played. Once your turn ends and it's your opponent's turn, the +3 attack wears off (i.e. the unit can't attack this way multiple times in the same battle).
3. Yes: wounds track the leftover health of the unit. Your example unit has attack 5 but only has 4 health left. The unit would be trumped and killed. If it did not have the wound token, it would receive 4 wounds, then attack back and kill the opposing unit.
4. So far as I'm aware, no; the unit is killed the moment it has "0 health" unless you have an ability or effect that "returns a killed unit."
5. I don't know if there is an order. I play it this way (don't take this as official though):
- Player A plays a unit.
- Damage is resolved, if applicable (it's still player A's "turn").
- Player B plays a unit.
- Damage is resolved if applicable (it's still player B's "turn").
- Repeat
According to the official FAQ, there is an opportunity to use an ability immediately before and immediately after playing a unit. This same FAQ is not clear on when damage is resolved during this procedure, but the rulebook seems to say that it occurs immediately after a unit is played, so I'd say this occurs before an abililty can be triggered (things like Metalworking are announced before the unit is played, for example).
Player A can play resource abilities and can heal only on his "turn." Culture or Great Person abilities that are meant as interrupts (i.e. used on Player B's turn) will say so.
6. In general, no. Most abilities will say that they can only be used once per turn (Animal Husbandry), but resource abilities can only be used once per turn as per the rules. This means that if you use the Metalworking ability in one battle, and then you get into another battle immediately after, you can't use it again, even though it's a brand-new battle.