The 'colored' refers to the people who are not white or has brown skin. People with color are treated poorly by most white people to the point that 'colored people' have a separate bathroom, separate church, separate seat, and etc. Meanwhile, 'white' refers to the white people. White people thinks that 'colored people' are inferior to them. In short, they are racist.
First of all, Katherine is one of the 'colored people', we know that people like Katherine are treated differently to white people. Secondly, Katherine is a woman. In my perspective, Paul cannot accept the fact that a woman is better than him. His pride, as a man, is hurt, which makes him mad. He thinks he is always right, that he's smart and Katherine is dumb because she is a person with 'color' and also a woman.
Because they were competing with Russia. Russia and USA were competing against each other, their goal is to be the first country to send people to the outer space. In my perspective, they are doing this so that their country would have a good reputation and also the title of "the first to". But USA failed to be the first country to successfully send a human into outer space, so they switch their goal to be the first country to send a human into outer space and bring them back to the earth safely.
Respect is the key to have a good relationship because with respect, we can win people's heart and have good connections. Without respect, people would not treat you nicely and would have a bad image of you. That's why, if you want to be respected, you must first respect others.