Let's back up a little bit. The new film from Ryan Fleck and Anna Boden is the first time we've ever met Carol, and it charts her journey from a warrior with a memory issue, battling for the Kree people, to insanely powerful superhero who fights for the good of all people. Along the way, she discovers that she's a human named Carol Danvers, a former Air Force pilot, and her adoptive aliens, the Kree, are the bad guys. Those shapeshifting Skrulls she's been fighting? Not evil parasites. They're an alien race just trying to find a home after being persecuted by the militaristic Kree. (There are some Israel-Palestine metaphors in there that will likely be debated.)
In an extended flashback, triggered by a black box Skrull leader Talos (Ben Mendelsohn) brings Carol, we see how she became superpowered while working with the Kree scientist Mar-Vell. Mar-Vell was hidden on Earth as Wendy Lawson (Annette Bening), basically building a plane that can travel to other galaxies -- technology that could save the Skrulls. During a test run, Wendy and Carol are pursued by the Kree, and crash. To prevent the Kree from getting her work, Wendy instructs Carol to destroy the plane's engine. It backfires, and she absorbs its power. That's when Kree soldier Yon-Rogg decides to bring her back to the planet Hala as a sort of pet project.
But that core wasn't really Wendy's trump card. She hid her most powerful tool in her space lab: the Tesseract, a.k.a. one of the Infinity Stones now in Thanos' possession. By the end of the movie, the Tesseract is safe (for the time being) with Nick Fury and S.H.I.E.L.D. concealed in the belly of the cat Goose, actually an alien called a Flerken. In the final post-credits scene, our dear kitty coughs it up like a hairball. Carol, meanwhile, has flown off into space to help the Skrulls establish a new community. Which is all to say: Carol probably won't be so confused when she is informed that these stones have created a major problem since she's already seen how powerful they can be.
On the subject of Nick Fury: In her journey of self-discovery, Carol becomes pals with the S.H.I.E.L.D. agent. Such good ones that she takes his trusty pager and outfits it with Kree technology so he can call her in a time of emergency. As we now know, he manages to signal her just in time before he gets obliterated in the post-credits scene of Infinity War.