Context is what something is contained of. So explaining the context of a story, means to explain what the story means, or what the story is about.
The most accurate revision of the sentence is the first option: <span>Most students use the Internet to research facts and statistics, to find images to use in papers, and to chat with friends.
This sentence avoids parallelism issues since the grammatical form is consistent throughout the sentence. All the verbs are in the same form (infinitive form) as indicated by the phrases "to research facts and statistics", "to find images to use in papers" and "to chat with friends".
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The other options are incorrect since the phrases in the sentence have inconsistent grammatical forms.
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