Why did Jean turn into a skeleton?
Long story short? It's probably a plot point or ongoing mystery.
There's a few of options. One, Nimrod did something similar to her offscreen that he did to Iceman. She was another of his priority targets, being another Omega level mutant.
Two, the Blightswill on Moira's blade had that effect on her. Blightswill is a drink from Otherworld that dampens mutants powers...but it's never had this kind of effect on mutants that I remember. So I don't think it's this. It's possible Moira has "concentrated" the effects, but it doesn't really track with what's happened before. Oddly, Jean probably shouldn't have been able to USE her psychic powers after she got stabbed, and I'm not sure why she could.
Or three...this was actually a psychic illusion and Jean isn't as dead as she looks. Given that both Jean and Professor X are around, psychic illusion hijinks are DEFINITELY on the table. I have a feeling something similar happened with Mystique. Also...Jean has a mini-series of her own in the future. So, either she didn't die, she's coming back pretty soon, or she's copied her mind into someone else's mind and is living inside someone else as a psychic energy entity.
What happened to Cyclops?
Where did Rogue come from near the end there?
Both of these are references to the Avengers/X-Men 2023 Free Comic Book Day issue.
Okay, time for some backstory. Cyclops was leading a team of "traditional superhero" X-Men and got publicly killed on a mission. He was easily brought back, but since the mutants were keeping the fact that they COULD bring anyone back at any time a secret from the general human public, Cyclops could no longer be the public leader of these X-Men. So, he created a new identity and costume, calling himself "Captain Krakoa". During the Judgment Day event, everyone on Earth finds out about the mutants' resurrection protocols and "Captain Krakoa" isn't really needed anymore. In the FCBD issue, a Orchis agent breaks into the X-Men's public base in New York and steals the Captain Krakoa outfit. Then burns down the X-Men's tree-fort base and beats up Cyclops. Throwing him off the equivalent of a 5 story building. We don't know who this guy is yet. Personally...he's kind of giving me Fantomex vibes, but we don't know for sure who he is yet.
Rogue was off saving Captain America from Orchis agents. They were just doing this to distract the other heroes so they wouldn't be able to make it in time to help Krakoa during their main attack. Also, "Captain Krakoa" shows up again...and blows up the Senate in Washington DC. Therefore framing Krakoa for attacking the USA.
And when did Xavier teach Ms. Marvel the Red Triangle?
I'm honestly not 100% sure. It's POSSIBLE this happened already in a past book, but I'm unaware of it.
Ms Marvel WAS on a team with...*SIGH* a time-travelling younger version of Cyclops. It's possible he taught her the trick during his time on the Champions.
Or Professor X could have just given her a lesson psychically during or after she got resurrected. It doesn't take him long to download information into other people's minds.