That's an idiomatic expression so it wouldn't translate the same way.
If this sentence is using 하십시오체, then why does it use 나 instead of 저?
Conversely, I've seen some suggested corrections in this course as well as in the Korean to English course which will use 저 with lower forms of conjugation (say, "먹어" as opposed to "먹어요" or "먹습니다". Why is this?
The suggested translation includes an optional "Please". Is there any logic to why you would or would not include it for the translation?
In other words, does something in the verb directly suggest "Please"?
I know in Japanese, you just add 'kudasai' (more or less). But as far as I can tell (and I could be wrong, of course), there isn't a word that accomplishes that in these sentences.
Yes, the "please" in the translation is inferred by the formality of the speech. In English, to make a sentence more polite, you can add the word "please" in most cases. In Korean, you instead change the way you speak altogether to be more polite and show respect. This high formality/politeness speech level used here is called 하십시오체.
So here, the verb used is 마십시오. See how the ending ends in 십시오? This is a very polite ending in Korean. If you were saying this same sentence to a friend, you would say just 놀리지 마, with no 십시오 or 세요 ending.
This sentence translates to "Don't tease me." But because it's written in a formal speech level, and because in English, this translation would sound very blunt and rude, we add the "please" which is not found literally in Korean to make it more equivalent to the overall meaning of the sentence.
I hope this helps.