I believe Fury said at the end that he expected Stark to blab everything, that it was a calculated move to get the Skrull off their guard by making them think they'd gained an advantage. So Fury intended his cover to be blown because the strategic gain was worth that sacrifice.
I have a hard time believing Carol is a Skrull. Her reactions toward Mar-Vell and the Kree just seemed too genuine.
So far, the heroes who've been replaced in the show seem to correspond to ones who were replaced in the comics -- Cap, Invisible Woman, Mockingbird. Looking over the Marvel Database summary of Secret Invasion
, it looks like there was temporarily an impostor Ms. Marvel, but I'm not sure for how long. There was also an attempt to impersonate Hawkeye, but it seems to have been abortive.