Does "live on" here mean something like "exist"? If not, what's the difference?

When do you use the phrase "gonna be"?

"Gonna be" is the same phrase as "going to be." We use these phrases when we intend to do something in the future or when we expect something to happen in the future. "Gonna be" is informal, however you can use this phrase around almost anyone since English doesn't focus on formality. Ex: I'm gonna be late tonight. Ex: It's gonna be a cold one tomorrow! Ex: She's gonna be a mom soon. Ex: We're gonna be famous one day.

Could you please tell me the episode of "George Washington and cherry tree"? Is there a moral in the story?

The story about George Washington and the cherry tree is a common myth about George Washington, the first president of the United States. According to the myth, George Washington received an axe as a gift on his sixth birthday and chopped down his father's favorite cherry tree. His father became angry at him and asked him if he did it. George Washington told his father the truth that he chopped down his cherry tree and explained that he could never tell a lie. His father's anger turned to love because of George Washington's honesty. No one knows whether or not this story is true, however it has become a common American myth.

What's the difference between "play", "drama" and "theater"?

A "theater/theatre" is an entertainment venue where things like plays and movies can be viewed. A play is a theatrical (acting) performance that is seen live, whereas a drama is type of serious play that is watched at a theater or through the radio, tv, or internet. Thus, you can think of theaters as a place for watching plays, plays as theatrical performances, and dramas as a type of play centered on serious topics. They are all related terms! Ex: Tickets for the new play sold out this weekend, I'm so crushed! Ex: I enjoy watching dramas over comedies. Especially tv dramas! Ex: I like watching movies at the theatre.

Is “select” adjective here? Is "select" used a lot like this?

Yes, the word "select" is used as an adjective in this sentence. Select is used a lot in the same way as this sentence since "select" means chosen. In this video, she is saying that the fashion sold at Forever 21 was only being placed and sold in chosen stores by the company.

I suppose we use the word "weird" a lot in casual conversation. But what would be good alternatives to replace it?

You should note that the speaker in the video actually says "weary" and not "weird." "Weary" is an adjective meaning to be tired, fatigued, or exhausted. It thus has a meaning quite different from "weird." However, to answer your question, you can use the words "strange," "bizarre," or "odd" to replace "weird." Ex: He's an odd fellow. Ex: This house is rather strange. I think we should leave quickly.