What is an independent clause? - a clause that can form a complete sentence that can stand alone as a sentence, having a subject and a predicate. Remember that an independent clause has to have a subject and a verb.
Now, your answers:
2. We wanted to help the man because he is helpless. (try to make it simple).
3. Mother picked up the dishes and placed them on the sink.
4. I am reading a book which my father bought yesterday.
6. Rahul was delighted with the result after it had been announced.