While there is (at least) one crisis icon in play, threat cannot be removed from the main scheme by any player. That means you cannot remove threat by thwarting (both by thwart events and basic thwart)
Can I remove threat from the main scheme with Psychic Manipulation if there is a crisis icon?
No. Because Psychic Manipulation is considered you thwarting, you cannot remove threat from the main scheme.
Does Marvel Girl remove threat from the main scheme, after she attacks a minion, when there is a crisis icon?
No. Marvel Girl cannot remove threat from the main scheme because there is a crisis icon.
Can Storm (Ally) move threat from the main scheme to another scheme?
No. Storm cannot remove threat from the main scheme because there is a crisis icon.