Is the expression "round and round" only used by children?

What is the meaning of "you know what" here?

"You know what" is an informal expression used to emphasize the statement that comes after it. It doesn't have a particularly special meaning on it's own, and is sometimes used to get someone's attention before speaking. Ex: You know what? I'm hungry. Ex. She's a great student. And you know what, she placed first in our whole school.

What does "palm of the hand" refer to in this context? Also, in what circumstances could I use it?

"Palm of one's hand" means you have complete control over someone or something. So in this context, once they gain their trust, they think they'll have control over them. It also has a similar meaning to "have them right where we want them." You can use this when the circumstances align and you're trying to control or manipulate someone or something to do what you want. Ex: The residents will be in the palm of our hands after they announce who the new Mayor is. They'll have to agree to the new building. Ex: Because he's so talented, he's got his parents in the palm of his hand. Ex: I have the board of directors in the palm of my hand.

What does "spelling tips" mean here? Does it mean "spelling error correction"?

"Spelling tips" are tricks, rhymes, and games that help a person remember how to spell a word. For example, when I was a child, I had a difficult time spelling the word business. My teacher taught me a spelling trick that helped me learn and remember it. She told me to say BUS-I-NESS. Learning to say the word business this way helped me to remember how to spell this word. Ex: The teacher used different spelling tips to teach her students how to spell. Ex: I before E, except after C is a very common spelling tip that children learn. Ex: Desert and dessert are very similar in spelling. A spelling tip is the word dessert has two s's because you want more and more!

How do I understand this sentence? Is this sentence connected to the previous sentence, like "we are not necessarily seeing that the vacancy rates kind of..."?

This sentence is a little odd. You are correct on how this sentence is connected to the previous sentence, "So, we're not necessarily seeing that- the-the drop: vacancy rates kind of increasing, and then, um, for the prices to come down." She says that under normal circumstances (without a pandemic), you see an increase in rent prices, and then you will see those prices come down eventually. I think she is struggling to put her thoughts out into words, which may be why it's a little confusing to understand.

What does observational comedy mean? Is it a type of genre?

Correct, this is a popular type of comedy (particularly in standup comedy). It's comedy based on observations of everyday life. You can understand it as being based on the premises "have you ever noticed?" or "did you ever wonder why?" A comedian might make an joke about something that might occur in one's everyday life, such as "have you ever noticed that the bus or train is never on time when you have somewhere important to be?" The audience might not have wondered about it before, but will immediately relate with the joke and recognize that such absurdities do occur in everyday life.