말을 잘 안하다: If someone doesn't talk/answer well, we use this phrase. It can be because someone is quiet or someone doesnt like to talk so much.
For example,
"Whenever I ask something, David doesn't answer me well." 내가 무엇을 물어볼 때마다 David은 대답을 잘 안해요.
"Is she usually quiet?" "Yes, she doesn't talk a lot."
"그녀는 보통 조용해요?" "네, 그녀는 말을 잘 안해요."
부끄럽다 is an adjective, 부끄러움(부끄럼)을 타다 is a verb form. 타다 means you sense something so you need an objective noun such as 간지러움(tickle), 더위(heat), 추위(cold). We use 부끄럽다 to describe your feeling about a certain situation but we use 부끄러움을 타다 to describe someone in general either you or the others. In this case we usually put 많이 infront of 타다.
저는 부끄러워요: I am shy.
저는 부끄러움을 많이 타요: (In general) I am a very shy person.