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."