果たして + [sentence] + だろうか / のだろうか 果たして + [sentence] + かどうか 果たして + [sentence]
果たして goes at the head of a question and casts doubt on it: "really?", "I wonder whether". It sits at the start of the sentence or clause, and the end is a question – だろうか, のだろうか, のか, or かどうか inside a longer sentence.
The doubt is a serious one, so 果たして suits essays, news commentary and careful speech. In conversation, ほんとうに本当に with かな does the same job: ほんとうに本当にまにあう間に合うかな.
In a statement rather than a question, 果たして means "sure enough": what was expected did happen. This use is literary and rare outside novels.
The adverb is a different word from the て-form of はたす果たす, "carry out": やくそく約束をはたして果たして means "keeping the promise".