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I am playing a game with a friend and we stopped it until I get an answer to some questions about the battle.  It may not be as bad as quadratic equations, but it's close.  My opponent finally has a Lost Soul to attempt rescue, and she presents Mighty Men (Red 10/10) from territory, with the Territory Enhancement Sword of the Spirit.. (per the big book, such an enhancement can be played on a hero in one's territory).  Mighty Men let her negate an evil or neutral card--she chose my Damascus fortress that let me draw cards and increase hand size by 1...Next, Mighty Men may band single-brigade red warrior, and she does so--in comes Ahimelek (red 4/5) with his own "Armor of God Territory Class enhancement,  Breastplate of Righteousness".  Finally, Mighty Men allows her to draw a number of cards = her Armor of God cards in play, which is 4.   We then went to Mighty Men's enhancement, which I hope is the right order.  Sword of the Spirit increases hero X/X (again, number of Armor of God cards she has in play), so now Mighty Men is 14/14. Then we move to Ahimelek who "returns an evil char. to owner's hand" and "Protects your warrior class heroes from capture." Both Mighty Men and Ahimelek are warriors.  She returns Syrian Marauders, with Darts (weapon evil enhancement) to  my hand.  Finally we get to Ahimelek's territory class enhancement, Breastplate of Righteousness which "Protects Hero from Brown and Gray brigades.  If hero enters battle (which he did) select 4 evil brigades. Negates Evil Characters of selected brigades. "  She chose Crimson, Black, Orange and Pale Green.
Now I block, with Fallen Warrior (black 2/2 warrior) and the first of many questions comes up.  Fallen Warrior gains cumulative abilities (*/*) of each Hero successfully blocked.  Do I successfully block  Mighty Men but not Ahimelek, because Ahimelek is protected from brown and grey and negates everything else except yellow? If so, I'm still losing, (heroes 14/15  to my ECs 12/12) and I looked up "Immune and Protect", and found the steps used when "two or more characters are affected by protect".  Well, At this time, only one character is affected by protect, right?---the Fallen Warrior.  So I'm not sure if any of that "formula" applies ... yet.    But since I'm losing I play the next enhancement, and I play "Babel" (1/3) and all evil characters holder chooses may enter battle.  So I empty my forces and send Huge Eqyptian (yellow 9/9), Angry Mob and Nadab (grey 4/4 and 5/5)---but then I'm reminded by my opponent--"WAIT!" she says.  "You played the Egyptian and he's enough to give you the lead and me the initiative."  So, I pull the Mob and Nadab back to my territory, recalculate and find I have 21/21.    So here we have called a time out until I can get a kind expert, moderator, etc.  to help me with this combat. 
  First, Is Ahimelek the only Hero that is protected (vs grey/brown) and has negate powers over all the other brigades but yellow?    Assuming my opponent plays an enhancement, if she plays it on Ahimelek rather than Mighty Men, will that make a difference "by the numbers?  More importantly, do I get to continue banding (from playing "Babel", assuming she doesn't negate it) and bring in greys (Angry Mob and nadab), Browns (Zeresh and Abiran) and/or Yellow (Jambres)?   This, I think is where the rule about two or more cards being affected by a "protect".  And here is where I'm having flashbacks to finding the area under a curve.
    Is there a simple way to explain how to calculate a battle like this?  I had always had the mistaken notion that if one character in a "banding" situation possessed a power (like protect), then it appled to all members of that band, but I seem to have mixed up the rules with some other CCG.    ANY help at all here is gratefully accepted, and we'll hold the game where it is until I get an answer.  People here are very quick with answering questions so I told her it wouldn't take that long and we can probably finish the game tomorrow night.
    Thank you.

I think The Schaefer covered most of that.

Identifiers only apply to the card they are on. The X identifier on Sword of the Spirit is separate from the X identifier on Mighty Men, and each card uses it's own identifier in the ability. I think that's confusion on Mighty Men's draw. But as The Schaefer pointed out, you band OR draw, not both.

Placed Enhancements (like the Armor of God) can be active outside of battle, so the increase of the character with Sword of the Spirit happens before it enters battle, and only lasts while Sword of the Spirit remains placed.

I'm not sure why that section of the REG says it only applies if 2 or more characters are affected by immune/protect - it applies whenever one side has partial protection.

You have to multiple calculations, in groups, for each set of protection (or lack thereof)

For the unprotected characters, you compare the total toughness of ALL cards on their side of battle to the total strength of ALL cards on the other side of battle. If the opposing strength is greater than their combined toughness, the unprotected characters are being defeated.

For the protected characters, you compare the total toughness of ALL cards on their side of battle to the total strength of cards THEY ARE NOT PROTECTED FROM on the other side of battle. If the opposing strength of the cards they are not protected from is greater than their combined toughness, the protected characters are being defeated.

If all characters on both sides of battle are being defeated, it is a mutual destruction.
If all characters on only side of battle are being defeated, that side is losing. Even if some of the other side is being defeated, if one character isn't, that side is winning the battle.
If some characters are not being defeated on both sides, it is a stalemate.

So in the situation with Mighty Men & Ahimelek vs. Fallen Warrior & Huge Egyptian:

Mighty Men's toughness (10) vs. Fallen Warrior, Huge Egyptian, and Babel's strength (2, 9, 1) = 10 vs 12 = Mighty Warrior is being defeated
*EDIT - Ahimelek and Mighty Men's toughness (10 + 5) vs. Fallen Warrior, Huge Egyptian, and Babel's strength (2, 9, 1) = 15 vs 12 = Mighty Warrior is not being defeated
Ahimelek and Mighty Men's toughness (10 + 5) vs. Fallen Warrior, Huge Egyptian, and Babel's strength (2, 9, 1) = 15 vs 12 = Ahimelek is not being defeated

Fallen Warrior, Huge Egyptian, and Babel's toughness (2, 9, 3) vs. Ahimelek and Mighty Men's strength (10 + 4) = 14 vs 14 = Fallen Warrior and Huge Egyptian are being defeated

Since all ECs are being defeated and the Heroes are not being defeated, the ECs are losing the battle and have initiative.

If you had completed the band properly (banding in Angry Mob and Syrian Marauders) and Ahimelek was somehow protected from gray:
Mighty Warrior now still being defeated (15 vs 21)
Ahimelek is still not being defeated, since he's protected from Angry Mob and Syrian Marauders

The ECs are no longer being defeated with the extra toughness (23 vs 14)

So that would be stalemate.

Mighty Men's toughness (10) vs. Fallen Warrior, Huge Egyptian, and Babel's strength (2, 9, 1) = 10 vs 12 = Mighty Warrior is being defated

Wouldn't it be Mighty Men's toughness plus Ahimelek's toughness as per your definition?

For the unprotected characters, you compare the total toughness of ALL cards on their side of battle to the total strength of ALL cards on the other side of battle. If the opposing strength is greater than their combined toughness, the unprotected characters are being defeated.