The second sentence uses parentheses correctly:
"The lampshade (which was a family heirloom) somehow survived the fire."
However, it has a small typo: "Some how" should be written as "somehow" (as one word).
The other sentences have issues with the correct placement and use of parentheses:
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"Jothan did not want anymore pumpkin pie) he felt sick already." - The closing parenthesis is incorrectly placed.
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"The two brothers (who had never gotten along decided to go on a hiking trip together." - There is a missing closing parenthesis before "decided."
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"Ted and Eli( Because they were expert campers lit the campfire in less than a minute" - The opening parenthesis is incorrectly placed and there is a capital "B" in "Because" that should not be there.
So the best option, after correcting the small typo, is the second sentence.