Is it possible for a person to believe (as the devils do), but not “sincerely” enough? For him to have so little “real” faith that he will not be saved, despite asking God for salvation? Is it possible that Jesus will say, “Your ‘belief’ was phoney. You never ‘really’ believed; you only thought you did. You never ‘really’ asked for salvation because your faith and belief were not genuine. You are a hypocrite and deceived yourself. I never knew you.”
The conditions you describe are not possible. In Matt. 7:7-8 Jesus said that all who ask will receive, all who seek will find, and to all who knock the door will be opened. That’s because Ephesians 2:8-9 tells us the faith that saves us is a gift from God, and is not of ourselves. Accordingly there can be no question of it’s sufficiency.
And while we’re on the subject, let’s clarify James 2:19. It says, “You believe that there is one God. Good! Even the demons believe that–and shudder.” The demons believe there is one God because they’ve seen Him, but nowhere does this verse or any other say they believe Jesus died for their sins and rose again. James was not saying the demons are believers. He was saying that believing there’s one God is not enough to escape the judgment. You have to believe Jesus died for your sins and rose again.