Should be. Report it if not accepted.

Yes, you can think of it that way. You can also think of it as "in english"

で in this case is marking the thing that is used to accomplish an action. You can think of it as 'by means of'.

I don't really see the relationship with what one eats.

手で食べないでください。 Please don't eat with your hands.

フォークで食べてください。Please eat with a fork.

The particle を would mark what one eats:

パン/ライス/すし　を食べる Eat bread/rice/sushi.

Your proposed phrase means 'Give me English' in a literal way (as it follows directly after the direct object marker), as if English is a tangible object.

英語で話してください should be acceptable. 英語を話してください is not technically incorrect, but it is less common to use this particle (again, as English is not a tangible object). It sounds more like ‘Say something in English’, rather than ‘Speak English’.

ください, when used by itself, with no other verb attached, is a verb meaning to give; confer upon.

When ください is used after the て-form of another verb such as 話す, it serves a different function, that of 'please do for me what was stated previously in the clause', or put more simply: 'please'. In these cases, you should consider ください as an ancillary or helper verb (for lack of a better term).

おねがいします and ください function differently. With おねがいします, the principal verb is regularly omitted. おねがいします is kind of a catch-all, which encompasses the assumed (by context) main verb. That is not true for ください.

Take the following sentence:
いいアドバイスがあったらおねがいします。-If you have any good advice, I request (it).
If you wanted to use ください, you should include the verb for ‘tell’, ‘teach’, ‘say’, etc.: いいアドバイスがあったらおしえてください。If you have any good advice, please 'let me know'.

One should also keep in mind that おねがいします sounds more humble/polite than ください, which is more direct/blunt.

If you want to explore the difference further, here are a couple of links:
https://www.youtube.com/watch?v=YMgXlcgj8Y8 https://www.thoughtco.com/what-is-the-difference-between-kudasai-and-onegaishimasu-3572604

1. Onegaishimasu should come at the end of the request clause.
2. When using onegaishimasu as an alternative to kudasai, the verb is omitted. ('Eigo de hanashite kudasai' vs. 'Eigo de onegaishimasu')
3. Eego → eigo
4. 'Eigo de shimasu' is saying 'I will do it in English.' The te-form of a verb is used for requests.

Yes. 話せる means to 'be able to speak'. The normal te-form of this is 話せて. 話せまして would be an overly polite form. Both would be wrong however, as you just want the plain te-form of 話す, namely 話して.

「英語で話してください」should be fine.

Indeed, it does.