What does "I bet ~" mean?

Isn't it necessary to put "have" before "ever"?

You are correct, the correct utterance would be "have you ever [something]?" However, in casual conversation it is common to drop the "have" when asking questions. In this video, the speaker has dropped the "have" for this reason, and it is quite normal to do so. It is generally common to omit words in questions, like "(Do) you want some pizza?" Ex: (Have) you ever seen a dog this cute? Ex: (Do) you wanna go for a walk?

What's the main difference between being "wise" and "smart"?

To be "Smart" refers mostly to knowledge and absorbing information. "Wisdom", or to be "wise", refers more to having good judgment and experience in situations and life. Ex: My son is so smart! He always gets good grades in school. Ex: Because she's experienced so much in life, Ruby is very wise.

What does "good" mean in this expression "baked good"? Could you give some other examples?

"Good" here is the singular of the word "goods" which is used for merchandise or products that are on sale. So "baked good" would be bread or cake, etc. Ex: Croissants are my favorite baked good. Ex: The bakery sells a variety of baked goods.

Why would people say "broken" to someone exhausted? Is it because the person's condition is so bad that it seems they will never function well again?

It's similar to that! It's not necessarily that they'll never function again, though. Technically and figuratively, something "broken" can be fixed. It does mean something like "lost all hope." But actually, the phrase used here is "broken down," which means worn out or in bad condition. Ex: That broken-down washing machine won't last more than a week. Ex: After pushing through the semester, I feel broken down.

As a ruler, what's the main difference between a "queen" and an "empress?"

The main difference between a "queen" and an "empress" is that a "queen" rules over a kingdom, whereas an "empress" rules over an empire. In ranking, an "empress" is slightly higher than a "queen" since an "empire" is usually bigger than a "kingdom." Ex: Although her rank was high, it was not high enough to be an empress. Ex: She became queen through marriage and not by blood.