Yes, the past and past participle form of "dare" is "dared", so your example sentence is grammatically correct. That said, the tone is extremely formal. You could make it a little less formal like this: When I was 7, I didn't dare sleep alone. And the tone could be even more conversational with a different verb: When I was 7, I was scared of sleeping alone.

This is an interesting question. I had to do a little research to answer it. "Dare" can be used as a modal verb, but it can also be used as an ordinary verb. As a modal verb it does not conjugate or have tenses. This is the same as words like "would", "could", "should". They have no past tense. In your example, "dare" is used as an ordinary verb, so it does have a past tense. Your example is not modal. If you wanted to use "dare" in a modal way you would have said something like this: "When I was 7, I knew that I dare not sleep alone".