It's a completely new combat.
Yes, and that has nothing to do whether the character has taken his first wound or not.
According to your interpretation once a character has taken any wound ever he/she is now immune to the first blood rule since there is no mention of healing back to full resetting the rule either.
The rule says, specifically, "The first wound received by a character..."
If the character is not wounded, then apply the First Blood Rule.
If the character is wounded, then any additional would is not the first wound, is it?
Consider the mechanics. Attributes are created using 2D. They average about 1D. And, the range is up to 15.
Thus, if there were no First Blood rule, characters would hardly ever be killed or seriously wounded. The player would take them to Minor Wound/Unconscious first. Average damage is 2D-3D.
Thus, the CT writers needed a rule to put some risk in there. The First Blood rule does that.
AFTER a character is wounded, his attributes are lowered. Thus, the normal pick-and-choose wounding with full dice is more lethal.
Thus, the First Blood rule exists.
If you read the rule carefully, and consider the above, you'll realize that what I'm saying her is true. The First Blood rule only applies to a character who is not wounded, regardless of any new fight or combat round.