Can I use "as the fact that" instead of "for the fact that"?

What does "articulate" mean? Could you give me some examples?

Here, "articulate" is a verb that means expressing an idea or feeling coherently; communicating and putting something into words. It can also be an adjective to mean the ability to speak fluently and coherently. Ex: We need to articulate the main idea so others can understand it. Ex: Sometimes I struggle to articulate what I'm feeling and thinking. Ex: I'm not very articulate these days.

What does "taffy" mean? Is it a common word?

Taffy is a type of sweet, sticky candy made from sugar or molasses. It is boiled in butter and pulled over and over until it turns glossy.

How can I use “cut down on something” and “cut down something”?

"Cut down on something" means "reduce", so you can use it when discussing something you are/would like to reduce intaking or doing. "Cut down something" refers to literally cutting something so that is no longer standing, like a tree. Ex: I would like to cut down on sugar, I eat too much of it. Ex: The tree outside of my apartment is getting cut down.

I don't get why "some" was used before "fresh air."

"Some" means an unspecified amount or number of a thing. English speakers often add the determiner "some" following the verb "get" in casual conversation. For example, if someone wants to go buy apples but the number of apples is unspecified or uncertain, they will naturally say "I'm going to get some apples." Here, we see that the verb "get" precedes "some." If you want to use the verb "get" with an unspecified number of something (like fresh air, in the case of this video), you can use "some." Ex: I want to get some milk and bread at the grocery store. Ex: I think you need to get some exercise.

Does "you were ever my best friend" mean "you were friends in the past, but not now"? What does "ever" mean here?

Yes. You are correct that she is referring to the fact that they were friends and now aren't. "Ever" here means at any time or at any point. So she's saying she's sorry that they were best friends at any point. Ex: Nothing ever seems to upset her. Ex: He doesn't ever eat his vegetables.