It's not as common as it used to be, but many people in Asia still prefer to live with their parents even after they're grown up. Is it common for western people to live with their parents as well?

What does "get" mean here?

"Got" is the past participle of "get." "Got" in this sentence means to have something. Hagrid is telling Harry that he has something for Harry and plans to give it to him. Ex: You got a package in the mail today. Ex: I've got one hundred dollars in my wallet. Ex: He got a bicycle for his birthday.

What does "NASA" stand for?

Great question! "NASA" stands for the National Aeronautics and Space Administration, but it's quite long to say, so "NASA" is easier. It's responsible for space programs and research in the USA. Ex: I wanted to be a scientist for NASA once. Ex: NASA's headquarter is in Washington.

What's "shape" mean here? Is this used as a verb here?

Correct, "shape" is used as a verb in this example. When you shape metal, you are manipulating it to create the desired shape. We can also use shape as a verb to describe the process of manipulating other objects, for example, clay. Ex: The ceramicist was having a tough time shaping the clay into a vase. Ex: The ceramicist couldn't manipulate the clay into the correct form. Ex: The gardener did a great job shaping our trees. Ex: The gardener cut the leaves of the trees into different shapes, and it looked really nice.

Would it sound awkward if I say "do" instead of "have" in this sentence?

Yes, it would sound awkward to say "do" instead of "have" since they're talking about the baked good he has with him. It's a possessive object, so "have" is used. Whereas "do" is an action verb, so it would sound awkward when talking about possessing an item. However, you could say "What do you have for us?" instead of "got". Ex: What do you have for us today, Dave? Ex: What have you got in your bag? => possessive objects

What does "palette" mean here? Is it referring to an artistic tool?

Here the word "palette" refers to a range of colours or a colour scheme. You are correct though, as it is also the board that artists use to hold and mix paint. The meaning of the word "palette" has extended beyond actual colours to include figurative colours. A musician can use a "palette" of tones and modes. Either way it refers to a selected number of things (colours, sounds etc) from all available options. Ex: I choose a palette of natural, earthy colours. Ex: He wants to decorate the living room using a palette of warm, bright colours.