Heaven and earth are great, but greater still is the kindness of the Communist Party; father and mother are dear, but dearer still is Chairman Mao.
This quote exemplifies the brainwashing and indoctrination experienced by young people in China after the cultural revolution. John Lennon once joked that The Beatles were bigger than Jesus, but Chairman Mao's similar contention was meant to be taken seriously and was never said in jest. Mao was said to be more important spiritually than God; whatever your God tells you is right or wrong, Mao can feed your spirit far more effectively and is a greater barometer of morality. However much you love your parents and they love you, they cannot nurture you the way that Mao can. Each of the most influential and important characters in life are overshadowed by Mao and children are raised to believe that he is everything. This is why they are incapable of any other thought and incapable of questioning what they are told.
We were proud of our precious red scarves, which , like the national flag, were dyed red with the blood of our revolutionary martyrs.
Ji-Li is explaining how the revolutionary martyrs were kept alive, and adored, by the regime. They were honored with great symbolism; the red of the Chinese flag, and the red of their scarves, (and the scarf mentioned in the book's title) is symbolic of their sacrifice. The wearing of such a symbolic garment almost deifies the revolutionary soldiers who died whilst fighting the Japanese. Seeing how they are honored and loved throughout the nation makes young people want to be just like them. Ji-li goes on to say that she feels that she let Mao down by not having been old enough to fight alongside the martyrs and she also wishes that she would have the opportunity to fight in the future so that she could be as brave for the country as they were.
I had many beautiful dreams. I dreamed of being an actress, holding bunches of flowers, bowing again and again to answer curtain calls. Until now I had never doubted that I could achieve anything I wanted. The future had been full of infinite possibilites. Now, I was no longer sure that this was still true.
There are two distinct points being made in this quote.
Firstly, Ji-li is pondering the validity of her dreams and their possibilities after finding out that she is not going to be able to try out for the dance troupe because her family will not pass a background check. Before the cultural revolution, enthusiasm, hard work and talent had taken her wherever she wanted to go, and her success depended only on her own efforts. Now she was not in control of her dreams and the success of them, because even though she worked hard and was one of the best dancers in her class, she would not get an audition because of her family's dubious political status.
Secondly, she is also aware that her dreams are now not entirely her own. The new regime is now able to tell everyone what their dreams may be. Ji-li may only dream about being what she will be given permission to dream of being; if the government do not want her to be an actress she will not be one, and so her dreams are somewhat redundant because she has no control over the process of achieving them anymore.