Learn Hardcore Japanese: nihongo de hanasite kudasai.

で marks the means or medium—in this case, the language you use to speak. You’re literally saying “speak by means of Japanese.” The particle に usually indicates direction, location, or the target of an action, not the medium. So 日本語に話す sounds unnatural.

Why is the verb 話す in the て-form (話して) here?

In Japanese, you make a polite request by taking a verb’s て-form and adding ください. So 話す → 話して + ください gives you “please speak.”

What does ください mean in this sentence?

Literally, ください means “please give (me),” but when attached to a verb’s て-form, it turns that verb into a polite request: “please do [verb].”

Why do we often see ください in hiragana instead of the kanji 下さい?

Both are correct. Writing ください in hiragana feels softer and more common in everyday communication, while 下さい in kanji can look slightly more formal or literary.

Where is the subject in 日本語で話してください? It seems missing.

Japanese often omits subjects when they’re obvious from context. Here, the implied subject is “you,” so there’s no need to say あなた.

Can I use another verb like しゃべる instead of 話す?

Yes. 日本語でしゃべってください is perfectly natural and has a slightly more casual, conversational tone.

How can I make this request more casual among friends?

Drop ください and just say 日本語で話して. Among very close friends you might add よ for emphasis: 日本語で話してよ.

How do I make the request more polite or formal?

You can use more honorific language, for example:
日本語で話していただけますか？
or even more politely:
日本語でお話しいただけますでしょうか？

If I want to say “Please speak in English” instead, what changes?

Just replace 日本語 with 英語:
英語で話してください。