My favorite TV show is *drum roll* The big bang theory which has a lot of new vocabulary, argot, and best of all is the comedy., funny moments.

This show is chosen by me because it has a lot of cool English vocabulary, jargon that you can learn from.

That is what you askre asking for, right?

Sidenote, lately I got really busy because of schoolwork, late-night meetings, and upcoming tests.

But mark my words, busyness will not stop me from learning a new word and making stupid grammatical mistakes.

My favorite TV show is *drum roll* The bBig bBang tTheory, which has a lot of new vocabulary, argot, and, best of all is the, comedy.

Very good. The punctuation errors you made are the same that native English speakers make - in fact, most people would consider these corrections "nit-picking", anyway :) I'm going to explain why I made them, but don't let that stop you from feeling confident! Your writing comes across quite natural!

The corrections: First, titles, including the names of TV shows, should be capitalized. Second, the general rule is to use a comma before the word "which" when it starts a clause. Then I added commas around "best of all", because it's an 'interruption' (this is technically called a "parenthetical element", but even most native speakers don't know that, haha. All you need to know is that, when you interrupt yourself to add an aside, like "and, best of all, comedy", commas surround the interruption). Finally, I removed "is the" from "...and, best of all, is the comedy", because you are listing things that the TV show has. It would be unnatural to say, "It has is the comedy". If you want to check your grammar when writing a list, you can always try writing it out in a longer form to see if the grammar matches, for example: "The show has a lot of new vocabulary, it has argot (excellent word, by the way!), and, best of all, it has comedy."

This show I chose this cshosen by mew because it has a lot of cool English vocabulary, and jargon that you can learn.

Although your meaning is clear, it doesn't sound natural to say that the show was chosen by you. The technical reason for this is that this sentence uses the "passive voice". Passive and active voice deal with word order, and, although native speakers don't specifically think about it, they naturally tend to use active voice and often avoid passive voice. Often, this is because active voice is more direct and to-the-point.

Your sentence actually offers a perfect example for this. You are the "actor" - the one making the choice. Without you making your choice, no one would be acting on the show, and this specific sentence would no longer be relevant. Therefore, most English speakers would use the more direct 'active' word order and place you, the 'actor', at the start of the sentence. "Binh took an action. Binh chose this show." The way you worded it is *not wrong*. It's perfectly understandable! But it is a little unnatural, because it's less direct. By placing the show at the start of the sentence, "Binh took an action. Binh chose this show," becomes, "This show was acted upon. It was chosen by Binh."

That is what you asked for, right?

"Asked" - Past tense

In this show, Sheldon Cooper, the main character, has a lot of friends despite his social awkwardness that, which is really cool to see because I'm also socially inept.

Edit:
I just read the note you included below your entry - yes, you're absolutely right! You can definitely use "which" here.

Original correction:
Very good! Grammatically, these should be two different sentences (or you could use a semicolon if you want), and, stylistically, I would contract "That is" to "That's" for a more natural sound, but, otherwise, good job.

Sidenote, lately I got've been really busy because of schoolwork, late-night meetings, and upcoming tests.

Edit:
I just read your notes section, and, to answer your question about "sidenote", I would say it's acceptable here. Personally, if I were going to say this, I might phrase it, "As a side note", instead, but what you wrote would be fine, I think.

Original Correction:
"Late-night meetings" - Plural

But, mark my words, busyness will not stop me from learning new words and making stupid grammatical mistakes.

Comma before the interruption (parenthetical element:) ) "mark my words" in "But, mark my words, busyness..."
"Words" - Plural
"Grammatical mistakes" - Plural