—I had some noodles _____ lunch. What about you?
—I had some chicken and rice.
for lunch 是固定搭配，意为“当作午饭”，故答案为 B。
The teacher seemed _____ what had happened,but he said nothing.
seem 意为“看来，似乎”，其后常跟名词、形容词、动词不定式等，这里应该用动词不定式，因此答案为 A。
The girl started to learn to play the piano _____ the age of five. Now she can play it very well.
"at the age of …" 是固定搭配，意为“在……岁时”。