2. Yes, your rephrase is correct. "By some miracle" means "through the action of a miracle".
3. A dangling participle is a participle or a participial phrase for which there is no logical noun to modify. Thus, it is a modifier that just dangles in a sentence.
Lighting a cigar, the car drove off the road.
There is nothing in the sentence for "lighting a cigarette" to modify.
Lighting a cigar, John drove the car off the road.
Another problem with participles is called a misplaced modifier (though some also call this a dangling participle). The proper noun or pronoun is in the sentence, but the modifying participle is in the wrong place.
Flying around a flower, John saw a bee.
John saw a bee walking through the park.
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