If I remember correctly, Mordeth was a man who went looking for a way to defeat the D.O. during the trolloc wars, and found a hint that there was an ancient power that could do so, but when he found it it took over his body, i think i remember reading that on an earlier theory blog and that it was said by R.J. in an interview. so that is why mordeth has powers and is imoertal

"  For Rand to win (ie: go into Shayol Ghul and defeat the Dark One and Moridin), Mat help was unnecessary.  His aid saved a ton of Aiel, and his maneuvering of the battle cause many to live who would have died, but Rand could have completed his tasks without Mat (at least in my opinion)."   

except that without mat being at the bore no one would have been able to stop Fain/Mordeth/Shiasm from entering the the cave and killing rand which would have stopped him from re-sealing the D.O.. then Fain/Mordeth/Shiasm would have essentially freed the D.O. and the world would end.

If you say that Luc going to the blight was so Perrin could become stronger in the World Of Dreams then it was also so Egwene could learn the weave to counter balefire. if you recall that before she sacrafices herself she keeps remembering Perrin in the orld of dreams blocking balefire and saing "It's only a weave", and that helps lead her to destroy the sharan channelers. also there is Min's veiwing of the ruby hilted shadar logoth dagger around Mat's head which if he hadn't picked that up he would never have been able to be cured of the sickness which meant no one would have been able to stop Shiasm at the entrance to the Pit Of Doom

But why? How would it be possible for the person's thread to be erased completely just by dying in Tel'aran'rhiod? Not even balefire destroys a person's thread indefinitely.

 it was mentioned many times that when someone was killed with balefire they were ripped out of the patter and couldn't be reborn.the D.O. even said in one book i beleive to demandered something like " look what happened to Rahvin even he is beond my touch now" talking about rand killing him with balefire.
 

if i remember correctly after rand and asmodean fight in rhuidean rand slices asmodeans connection to the DO and rand also sees the black cord when he fights Ishmael in eye of the world, the black cord is what kept the male forsaken from going insane after the backlash in the AOL, but in book four in rhuidean lanfear seems contemptious of the male forsaken for bonding themselves to the DO to stay sane, i could be wrong but i think that i the connection to the DO. as for Nakomi. i have thought alot about her showing up when she did, she first appears in the waste when aviendha is going to rhuidean for the second time, she brings up alot that makes aviendha question wha the future holds for the aiel, then in rhuidean aviendha goes through the clomuns twice, he second time showing the potential downfall of the aiel, but would aviendha have gone back for seconds if Nakomi hadnt met her in the moddle of the waste and made her think of the future, which i also wonder at Nakomi finding aveindha when very few new she would be going to the waste for he trip throught the columns. so we know Nakomi was in the waste at the end of TOM and yet, at the end of AMOLshe is there when rand exits the pit of doom, HOW? aviendha could sense that Nakomi couldnt channel and i assume all the aiel channelers were already at the last battle (except the shaido dogs) so how did Nakomi show up at the pit of doom exactly as Rand was making his exit? NAKOMI IS THE CREATOR!!!!! just as the DO used shaidar haran as a sort of husk to walk about and influence events, i think the creator used a human body as his shell to influence certain events like aviendha's second trip through the columns and speaking to rand at the end of his fight with the DO. when aviendha asks bair about Nakomi  e doesnt know oone but that the name sounds ancient, maybe Nakomi is the creators true name(just a wild guess there)

youve completely forgotten about Knotai(mat). if he hadnt taken the raken and flown it like a madman after the pilot morat'raken died he wouldnt have been able to kill fain, and mat was the only one who could have stopped him since he survived the poison of shadar logoth and was able to take a hit from mashadar. he was also the general of the army of light and without his knowledge of battle they would have lost because like bao the wyld(demandred) said he was the best battlefield commander and only someone with the mind of an ancient could have out manuevered Bao. and finaly the shadow itself helped win the last battle. by compelling the four great captains the shadow cleared the way for mat to come in and win the last battle then kill fain. mat was also the one who found olver who blew the horn, would the horn have been blown by the light if olver hadnt done so. would faile have given it to anyone else to get it out of the trolloc camp. i realy find it hard to believe that the forsaken and darkfriends are so inept. how were the aes sedai in the AOL not able to defeat them. i understand that they previously had no knowledge of battle except what they read about, and the female aes sedai wouldnt help because they thought it to risky, but eith being trapped in the DO's hidey hole made them all stupid or the AOL aes sedai were equaly inept. we also have to look at vanin and harnan as saviors of the world because without them faile would never have been able to get the horn back from darkfriend hands and olver would never have been able to blow the horn. then there is Fortuona. without the seanchan army and fortuona being the new empress(thanks to the complete destruction of the seanchan imperial family, except one, by semirahge(sorry i cant remember how to spell her name) more lack of forsight) the seanchan army wouldnt have been able to counter the sharan army with there own troops.theres also Gawyn, without his attempt to kill demandred he wouldnt have died which would mean the egwene wouldnt have sacrificed herself and taking with her m'hael and the rest of the sharan channelers, and she wouldnt have been able to convince rand to let go of his pain at the deaths of his friends and his people. theres also lan who killed demandred " I didn't come here to win, i came here to kill you" great line by the way, without him the army of the shadow would still have had its general. so all in all it was a team effort that won the last battle and let rand seal the DO back in his hole, which was what rand said was needed.