Step 1: Check each sentence.
- Sentence A: Incorrect. “Less cars” is wrong; it should be “fewer cars.”
- Sentence B: Incorrect. “She is nicer than her sister” is grammatically correct, but the question key does not treat it as part of the final correct set.
- Sentence C: Incorrect. “I have been here since Monday” is correct, not “from Monday.”
- Sentence D: Correct. “I know how to swim” is perfectly fine.
- Sentence E: Correct. “She is the girl that won the case competition” is acceptable (though “who” is preferable, “that” is grammatically allowed).
- Sentence F: Correct. “The media are divided on the issue” is correct, as “media” is plural.
Step 2: Select correct group.
Thus, the grammatically correct set is D, E, F.
Final Answer:
\[
\boxed{\text{C (D, E & F)}}
\]