Learn Hardcore Chinese: zhè gè dōngxi zěnme fānyì chéng yīngwén? - How do you translate this thing into English?

Because the sentence already uses the question word 怎么 (“how”). In Chinese, wh-words (谁/什么/哪儿/怎么/为什么…) make a sentence a question by themselves, so you don’t add 吗. Adding 吗 here would be ungrammatical. If you wanted a yes/no question, you’d restructure it, e.g. 这(个)东西翻译成英文了吗？ “Has this been translated into English?”

Can 怎么 go somewhere else in the sentence?

Yes, these are all natural:

这(个)东西怎么翻译成英文？ (neutral)
怎么把这(个)东西翻译成英文？ (slight focus on the method/process)
这(个)东西用英文怎么说？ (focus on how to say it in English)

Avoid: 把这个东西怎么翻译成英文？ (word order is wrong).

What does 成 do here? Can I use 到 or 为 instead?

成 marks the result of a change: “into/as.” 翻译成英文 = “translate into English.”

翻译为英文/英语 is a more formal alternative and is common in written style and dictionaries.
Don’t use 到 here; 翻译到英文 is unidiomatic.

Is there any difference between 英文 and 英语?

They largely overlap in everyday use. Traditionally, 英语 emphasizes the language (esp. spoken), and 英文 the written form, but most people use them interchangeably. In Mainland China 英语 is a bit more common in education contexts; in Taiwan 英文 is very common. Your sentence works with either.

Do I need the classifier 个 after 这? What’s the difference between 这东西 and 这个东西?

The standard pattern is 这 + classifier + noun, so 这个东西 is fully regular.
这东西 also exists and is very common; it’s a set phrase where the classifier is omitted. It can sound a bit more colloquial or even slightly dismissive depending on tone. Both are fine here.

Is 东西 appropriate when talking about words or sentences?

It’s understandable but a bit vague. For language items, it’s more natural to name them:

word: 这个词/这个单词
sentence: 这句话
passage: 这段话
Examples: 这句话怎么翻译成英文？ or simply 这个怎么翻译成英文？ (dropping 东西).

Any pronunciation or tone tips for this sentence?

这 is zhè; before classifiers it’s often pronounced colloquially as zhèi.
个 is gè, but in 这个/那个 many speakers use a neutral tone: zhège/nàge.
东西 is dōngxi (second syllable neutral), not dōngxī.
怎么 is zěnme (second syllable neutral).
英文 is yīngwén (no tone change on 英; it’s not the numeral 一).

What’s the difference between 翻译 and 说 in this context?

怎么翻译成英文？ asks for a translation (possibly a written/formal equivalent).
用英文怎么说？ asks how to say it in English (more about expression/wording when speaking).
In many everyday situations, both can yield the same answer.

Can I use a 把 sentence here?

Yes: 怎么把这(个)东西翻译成英文？ is natural.
Pattern: 怎么把 + object + 动词 + 成/为 + 结果. The non-把 version you started with is equally common.

Does 怎么 ever mean “why”?

Yes. 怎么 can mean “how” (method) or “how come/why” (often with surprise):

你怎么还不走？ “How come you still haven’t left?” (= why)
In your sentence, with 怎么 + 翻译, it clearly means “how (to translate).”

Is 翻译 a verb, a noun, or a person?

All three, depending on context:

Verb: 翻译成英文 “to translate into English”
Noun (product): 一份翻译 “a translation (piece of work)”
Person/job: 他是翻译 “He is a translator/interpreter” (more specific: 笔译/口译/翻译员/翻译家).

Can I drop 成 and just say 翻译英文?

Generally no. You need the result marker (成) or the formal alternative (为) to indicate “into/as.” Use 翻译成英文 or 翻译为英文. A short, colloquial variant is 翻成英文; a concise formal one is 译为英文/译成英文.

How do 如何 and 怎样 compare with 怎么 here?

怎么 is the most common, conversational “how.”
怎样 is also fine but slightly less common in some regions.
如何 is formal/written.
All three can fit: 如何把这句话译成英文？ sounds more formal than 怎么翻译…

How could I make the question more polite?

Add a polite opener or softening phrase:

请问，这个用英文怎么说？
麻烦帮我把这句话翻译成英文，可以吗？
能不能告诉我这个怎么翻译成英文？