to my opinion, only sentence 1 is correct. Sentence 3 should be written reversing the clauses of the sentence: 3. "she knew that it was dangerous; she walked home by herself, though. In this case, "though" is an adverb, with the meaning of "despite this". So, that "this" must be specified in the first clause.
Anyway, wait for confirmation of a native speaker, please.
PS. Another way to express the sentence with "though": "Even though she knew that it was dangerous, she walked home by herself". In this case "even though" is a conjunction, and the order of the clauses can be reversed: "She walked home by herself, even though she knew that it was dangerous, "