2. The medicine was administered to the patient to _____ the disease which made him ill. 1.?

#1 and #2 are not even words, and #4 only refers to money or art. That leaves #3, but that is not a correct usage of the word.

If you have an itch, almost any kind of oil or moisturizing cream will counteract the itch, but it does nothing to eliminate the cause of the itch. A medicine cures the cause of the itch, but maybe does nothing to relieve the itch. So you are talking about different actions on different subjects.