Is there a difference in saying between "are you willing to say" and "can you say?"

Maybe the script should be "No minor's allowed"..? Because I thought "minor" should be singular here.

"Minors" is correct here. "Minors" is used because anybody who is under the age of 18 is a "minor". Because this refers to more than one person (because more than one person who exists is under the age of 18) "minors" (plural) is used.

Is there a difference in saying between "are you willing to say" and "can you say?"

There's a slight difference! "Are you willing to say" means to ask if someone WANTS to say something, whereas "can you say" indicates ability, such as restrictions or risks outside of someone's control, like a work contract or something like that. Ex: A- Are you willing to say what side you agree with? B- I'm willing. But according to my contract, I can't. Ex: Can you say what side you agree with?

What does "fall apart" mean? Is it a common expression?

"Fall apart" is a common phrase! It has a couple of meanings. It either means something comes apart or disintegrates, or it means losing one's ability to cope emotionally. Here they're using it to refer to emotions! Ex: I fell apart when they played the last song at the wedding. = I cried when they played the last song at the wedding. Ex: Jane's gonna fall apart soon. = Jane's gonna have an emotional breakdown soon.

What's the "dark web?"

The "dark web" refers to the part of the World Wide Web (the Internet) that isn't available through search engines and can only be accessed through special software or browsers. People use the dark web use to make sure their activity remains anonymous or untraceable, like criminals or spies. Ex: You can find a lot of creepy, scary stuff on the dark web. Ex: The dark web can often be a haven for criminals hiding from police.

What exactly is the "Tea Party" in American politics?

From my understanding, the "Tea Party" in American politics is a conservative group of republicans that formed in 2009. Their goals are economical. They want to limit government. They oppose excessive taxation, and they support immigration control. Ex: The Tea Party group started in 2009. Ex: We, the Tea Party, believe the government can't tell you what foods to eat. => reference from the video.