In the movie Robots, Herb tells Rodney, "You've got greatness in you, Rodney. Never doubt it." That means, "Never think it's false that you've greatness in you. Never think it's untrue!"
If you’re doubtful, you’re thinking that something is not true or that something won’t happen. If you said, "Miss Liesl, I couldn't do my homework because I got sucked up in a tornado with 92 cows," then I would be doubtful!
If you doubt yourself, that means you don't believe in yourself: you don't think you're smart enough or strong enough to do something. If someone tells you, "Don't try out for the basketball team; you're not fast enough," then don't listen. Don't doubt yourself! Believe in yourself.
Something that's doubtless, or undoubted, is definitely true, or definitely will happen, and nobody questions it: nobody thinks it's false, or nobody thinks it won't happen. Lindsey's musical talent is undoubted. That means, nobody questions it: everybody knows that Lindsey is a talented musician. We often use "doubtless" as an adverb, like this: "Lindsey's show will doubtless amaze you." Or, "She will doubtless impress you with her performance."