1. Though the baby was left alone, she didn¡¯t cry.
2. Left alone, the baby didn't cry.
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Can #1 be changed into #2? In #1, the baby was a girl, but in #2, we cannot know the gender of the baby. In this case, what is the suitable participle phrase for #1?
Both are fine, but there's no way to indicate in a participle phrase what the gender is. You'd have to say "the baby girl" in the main clause to indicate that the baby was female -- or "the baby boy" to indicate he was male.
Yes, you can change sentence #1 into sentence #2. Both sentences convey the same meaning, indicating that the baby was left alone and did not cry. However, you are correct that sentence #2 does not specify the gender of the baby. If you want to maintain the gender of the baby as a girl in the participle phrase, you can use "Being a girl" as the suitable participle phrase for sentence #1:
"Being a girl, the baby didn't cry."
This way, the sentence retains the information about the baby being a girl, while still expressing the same idea as in sentence #1.