: How does one include non-Latin-based script in an overall English work? For Latin-based languages, the foreign term may be expressed in italics. Gracias. However, what about non-Latin-based languages

I'm posting a second answer because this suggestion is a little out there, but it might be a way to have your cake and eat it too.

If you are publishing a cybertext, make the bilingual stuff interactive. Any website or e-reader should be able to handle basic javascript that would allow the reader to click on the words and swap them for another text.

One example is Stone Harbor by Liza Daly. It has words that are replaced when they are clicked.

Consider it a feature of the story. Clicking or not is voluntary. You could also create a preference system where they are set one way or the other by user choice.

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How does one include non-Latin-based script in an overall English work?

Not like that.
As Galastel noted, you're wasting space in a medium of bare-bones verbal communication on not-especially-attractive artwork. Look at this sentence:

Using 漢字 in English running text is so disrespectful to the average reader that you are drastically shrinking the potential reach of your message.

In that sentence, context clues probably told Gal exactly what those flattened spiders in the middle were supposed to mean. In none of your three examples is that the case. I mean, ok, we do know the middle one is supposed to be some kind of imprecation but

(a) You're not telling them if this is an annoyed Australian 'cunt', a snotty British 'wanker', a career-risking American 'cunt', or a career-ending American [racial slur].

(b) You're telling them nothing about the actual word or the culture behind it.

They're not going to guess that it's an agricultural-based insult that's older than their civilization—in America's case, by an order of magnitude. They're not going to know how to say it or how to use it. They aren't going to feel closer to Chinese culture because you pushed them away. Look at this sentence:

Using hànzì in English running text accomplishes literally nothing beneficial, compared to giving your readers a toehold with transcriptions that they can at least sound out in their heads.

People can read that, maybe even notice the tones. They might use it to sound knowing at a business meeting or to talk about their friend's new tattoo. They're learning something, in a medium they'll be able to remember and use.
If people wanted to abstractly contemplate the beauty of Chinese script, they'd want to see a work with photographic reproductions of calligraphy, not snippets of Microsoft Office's MS宋体 font. If you were telling a story between the panels of that calligraphy, you could do it in text but you'd be better off writing and illustrating a graphic novel. Sandman, Samurai Jack, and Apocalypto could go a long way in gibberish or silence or incomprehensible dialect because they leaned heavy on visuals and mood.
Who's your audience?
Now, sure, there's a time and a place for it. If you are completely uninterested in reaching out to the general American, British, and international English market, you're going to have trouble finding a publisher but you can self-publish and you can crowdsource and niche market and you can tell a story to the bilingual about the lived bilingual experience. That's not nothing. Kick some butt and 加油！
But they probably aren't the ones who would benefit from hearing about wacky misunderstandings with tones or who are interested in just what that unpleasant Shanghainese banker just called them. How are they even supposed to understand the point that you're making about tones if you're using characters?

'.' Zhang Wei leaned over. 'Dude, she's your , not your .'

is more comprehensible than going '媽麻馬罵吗'. At least with Egyptian hieroglyphics there are pictures to latch onto. Meanwhile, a paragraph of analogies can introduce your readers to tonal languages, explain the modern system in Mandarin or (with a few more paragraphs) Cantonese, and make it perfectly clear what's happening to the sounds in the nonsense series mā, má, mǎ, mà, ma.

If the entire work is written in English but some dialogue has to be in Mandarin Chinese to illustrate the character's mistakes while speaking Chinese, then is it okay to just include Mandarin Chinese in the text?

Using Chinese characters brings so little to the table that it's generally going to be clearer to just use English for most of your Chinese references and use pinyin transcription for the details.

You do not need to give the pinyin, let alone the characters, to explain your characters' mistakes. You can—with greater effect for most readers—just directly explain whatever the mistaken words mean in English.
Saying the Chinese character for 'peace' is 安, composed of 女 under a 宀, is far less evocative—even in calligraphy—than discussing how hard it can be for a modern woman to be a daughter-in-law in a culture where the character for 'happiness' is a woman with a baby and the character for 'peace' is a woman confined to her home. You shouldn't just turn 对牛弹琴 into 'pearls before swine'—that takes all the charm and setting out of the scene in favor of a tired cliché—but you should introduce them to at least the idea of a cultured nobleman, centuries past, mad from watching his civilization consume itself in civil war, playing his delicate zither amongst the cows.
I think those are the only two directions to go:

to either speak directly to the 1st- and 2nd-generation Chinese immigrants to the English-speaking world and hope they like you enough that there's a career in it or
to keep yourself accessible to the 'illiterates' who will need handholding as you guide them into authentic Chinese language and culture

Having said that...
That's true if you're writing books. Everything I've just said can be ignored with minimum fuss if you're publishing online or via some mobile app platform that allows scrollover or clicking to produce instant glosses of the moments when you use characters.
Chinasmack seems to have lost the functionality, so I won't bother linking, but it used to provide translations of Chinese social media with the original Chinese text available on scrollover; you would just go the other way. It allows immediacy and immersion but still quickly provides the 'subtitles' that your readers need to follow your message.

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Transliteration is commonly used in cases such as you describe. Look for example at Ken Liu's short story Mono no aware: the title itself is a transliteration. Then, within the text, there is an explanation:

“Everything passes, Hiroto,” Dad said. “That feeling in your heart: It’s called mono no aware. It is a sense of the transience of all things in life.”

Your Chinese characters are utterly meaningless to me, as they would be to any non-bilingual reader. They are pictures, and unlike emoji, they convey to me nothing whatsoever. Transliteration is the only way that would allow me to have an idea of what sound they're supposed to make.

Thus, the only reason I see to include actual foreign characters is if you wish to talk about their shape. For example, from Mono no aware again,

The world is shaped like the kanji for umbrella, only written so poorly, like my handwriting, that all the parts are out of proportion. [followed by an image of the relevant kanji]

Such use is actually beautiful, since it conveys foreignness without distancing the reader.

Your text should be readable, understandable, and enjoyable for an audience that speaks no language except for the one you're writing in.

What to do when it's important that your character makes mistakes in another language? This is a case for telling rather than showing. From Mono no aware:

My father would be greatly ashamed at the childish way I still form my characters. Indeed, I can barely write many of them anymore. My formal schooling back in Japan ceased when I was only eight.

I cannot tell from the drawing of the kanji that anything is wrong with it, but the MC tells me it is wrong.

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Think what you would do the other way around. If the entire book were in Mandarin Chinese and you had an English speaking character - would you print their English in Latin-based script, it would you convert the sounds into Mandarin Chinese script phonetically?

I don't know the answer to that question, but my guess would be that in order to make it easier for your (primarily) Chinese audience, you would give them the words in the Mandarin Chinese character equivalent. This would give them a better chance of working out the meaning. But, like I said - I don't know.

So, to go back to your question. For me it's all about how easy it would be for me, as an English speaker with very little Mandarin Chinese, and virtually no expertise in Mandarin Chinese script, to find the meaning of those words.

If I were reading a paper copy of the book - because I don't have a Mandarin Chinese keyboard, I would be unable to look up the words printed in Mandarin Chinese on the internet. However, if they were rendered in Latin script as the phonetic equivalents of the Mandarin Chinese, then (provided the spelling was relatively accurate) I could look up the words up on the internet.

If I were reading a digital copy then it wouldn't matter either way, because I could just copy the phrases and paste them into a search engine either way around. Some software even allows you to do that from the book-reader. In that way, I would be able to find the meanings quickly and easily.

So, in conclusion - I would use the phonetic equivalents of the Mandarin Chinese phrases, printed in Latin script in order to give the readers a better chance of finding meaning from the Mandarin Chinese words and thence from the book.

Good luck with your writing - I wish you success whichever method you choose.

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It sounds like you have some specific examples in mind where the whole point of the exchange is the language barrier. It could be an opportunity to trigger empathy in the reader, either as the bilingual or the monolingual who misses part of the conversation.

I live in a cosmopolitan city. Half the writing I encounter in a daily commute is in an alphabet I cannot read. I do not feel threatened by it, and it seems more authentic (to me) to allow the characters to communicate as they themselves "see" the communication. If I can't read it, yeah I feel a little stupid like there is something I am missing, and I wish I could read everything with full fluency – but that's not the world I live in, and sounds like that's not the world your characters live in either.

It's the age of Unicode. People are communicating in emoji. Yes, you should feely use all the alphabets that are available to us in this amazing time of instant and flexible (and bizarre) communication. Based on some of your examples, it seems the subject matter is self-evident of what lingual-separation means. It's a part of your story. Use the alphabet as a story mechanic, to reflect the situation.

We don't write dialog phonetically, unless it's about the sounds a person hears without understanding the words. When people speak with an accent, we don't write each word phonetically in their accent, we write what they intended to say, or whatever gets the meaning across in the least distracting way. You can probably search for styleguides that combine alphabets, but I suggest you decide on your own rule and stick with it throughout the story. Whatever you decide the reader will adapt, just be consistent.

My suggestion is to not explain everything to the reader. Sometimes when romance languages are done in italics it becomes cloying and condescending – the conversation is being dumbed down for the reader, not the other characters. I can get meaning from context if the emotional situation is clear.

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