小题1:A serious illness(did).
小题2:Difficulties/Problems/Troubles/Challenges
小题3:She swam a ten-mile marathon and set women’s record.
Or: She swam a ten-mile marathon, setting the women’s record.
Or: She set the women’s record for a ten-mile marathon swimming.
小题4:Because she had tried her best ( to fulfill the task .)
Or: Her strength of purpose was as important as reaching Cuba.