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What if Jean Grey died, and stayed dead the first time around...in effect several X-men left the team: Colossus persued art in Paris, Nightcrawler studied in a monestary in Sweden, Storm returned to tend to her tribe in Africa, and Xavier remained with Lilandra along with Wolverine- who's appointed Captain of the Imerial Guard.
Cyclops goes to Alaska to sort out his life. While at a ski resort he encounters a beautiful British woman, Elisabeth Braddock who'd been blinded in battle as Captain Britain. The two struck up a conversation about their mutant powers. Betsy, as she sweetly asked him to address her, was a telepath and didn't need eyes to see Scott's pain.
Suddenly she screams, a frantic energy pattern jolts from her soft countenance in the shape of a butterfly. She falls to the floor mumbling "they're already here"
....She awakens in an infirmery, two furry fingers taking her pulse. "You must be Henry." she says. Beast assures her that nothing's wrong physically, but Cyclops wants to know who "they" are. She then remembers her precog flash, an alien invasion, already pending and to stop it, they must assemble a new team of mutants. Cyclops says he'll just call in the other members, but Betsy (using Jean Grey's mental residue to contact the X-Men through Cyclops) sensed they had already become hosts.
Using Cerebro she assembles:
Thunderbird (who hadn't previously joined)
Quicksilver
Scarlet Witch
Gambit
Magma
Sunspot
Feral
with herself, Cyclops and Beast rounding out the team...
more tomorrow

Why would the Shi'ar elect Wolverine to be of the Imperial Guard? He'd probably spend the time to figure out his past (or get a girlfriend).

Unless he is brainwashed or Cyclops is more persuasive than I give him credit, Thunderbird might be too stubborn to join (it took Xavier classifying him as a wimp to join).

Quicksilver and Scarlet Witch might be obtainable as this is after they separated from the Brotherhood of Evil Mutants.

This probably pre-dates Gambit's association with the Marauders, but he might still be with the Thieves in preparation for the union with the assassins and probably wouldn't join.

Magma might be a little too young and Sunspot wasn't even a New Mutant yet, so he's also inexperienced.

Feral would be a danger to the group (she killed her mother).

I'm unsure of whether the Kwannon or Betsy was the one truly attracted to Cyclops, so I do not know whether this relationship would arise (what's so special about Cyclops anyway?).

Which incident is occurring also? I'm trying to remember exactly what threat was occurring at the time, but I'm drawing blanks.

this is all hypothetical, after jean's death (phoenix force never put her in suspended animation, instead continued using the real thing) and was actually killed by the Shi-ar laser.
Xavier decides to stay in space and a disheartened Wolverine accepts Lilandra's offer to join the Imperial Guard.
I sped up time just a little bit, (new mutants would be about 15) and decided to introduce Psylocke and Cyclops at a ski resort...
(In the comics, Betsy went skiing to take her mind off of her ordeal with slaymaster/ Cyclops always went to Alaska to clear his head, so they just happen upon the same lodge)
The precognitive flash Bets experiences fortells the invasion of Earth by the Brood (who are obviously coming a little bit earlier than on 616)
To answer all of your questions (and I'm sure you won't like the answers, but I'll have to remind you that this is a different timeline and the absense of a single raindrop can change an entire series of events.)
1) already answered, wolvie doesn't want to walk on an earth that 'red' doesn't tread on.
2) yeah, my lineup doesn't make a whole lotta sense considering the immediate danger, guess they'd all need to be in the area. I like the idea of keeping Thunderbird alive though...maybe the threat of losing his people to the Brood would send him into battle.
3) in this timeline, Wanda's powers weren't transformed by magic and she inheritted her father's magnetic might, going by Polaris (green haired polaris never existed) she and Pietro parted ways with Magneto, turning his own powers against him, in effect killing him and the brotherhood, when Betsy contacts them, they're in New York applying for the Avengers.
4) at this point, Gambit's already been battling the Brood in the bayou. they've taken out most of his thieves including BellaDonna. He and his fellow thief, Hound (psionically linked w/ 3 dogs) are in Mississippi when he intercepts a telepathic S.O.S. and heads towards the signal using his 'luck'
(if you haven't noticed, i'm kinda making this up as i go)
5) let's forget magma and sunspot, i've already added Hound, so lets sub fire for Iceman and leave it at that.
6) Feral's dad never left and she lived a happy childhood, dreamed of being a cop when she grew up, but when her powers manifested, she became a recluse tending to the pigeons on the roof, then she got the call...
7) we all know Cylops has a thing for telepaths, kind of capitolizing on that fact. i'm not saying they'll get together...they're both just very vulnerable, and they're about to have to defend the planet on top of all else.
So...Cyclops, Beast, Betsy, Iceman, Polaris(Wanda), Quicksilver, Gambit, Hound, and Feral(14)