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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