"I eat lunch at a restaurant."
Don't know about fluent, but...
レストラン: Restaurant で: Particle to indicate that the action is happening at the just-stated location (the restaurant) お: Honorific (because you need to be polite to your lunch, apparently) ひるごはん: Literally 'day rice', the Japanese term for lunch を: Particle to indicate... Something. I think it's the passive sense, but I haven't really internalized that part yet. In this sentence, it indicates that the action is being applied to the part of the sentence that was just said. 食べ: To eat ます: Auxiliary verb, here used to conjugate the other verb into an actual action, or something. At any rate, when it you add ます or です to the end, you're sayng that things are happening (as opposed to asking about it (ですか) or saying it is not the case (ません))
This is basically correct, except for the following details:
The function of を is to mark the grammatical (direct) object, which as you say is the thing (this may include people) that is being acted upon or directly affected by the action.
ます is not an auxiliary verb, it is an ending (like English -s or -ed) which says that the verb is in non-past tense (present or future), positive (that is, not negated) and in the polite form. (We know that it isn't an auxiliary because it cannot stand on its own, like です can.)
The question particle か can be used with any form of any verb and should not be conflated with です: 食べますか "Do you eat?", 食べませんか "Do you not eat?", 食べましたか "Did you eat?", 食べませんでしたか "Did you not eat?", and so on.
Yes. Putting the object (ひるごはんを) just before the verb is the "neutral" word order, so if you put anything else between them that part becomes emphasized: "I eat lunch at a restaurant" (as opposed to, say, at home, in a cafeteria or from a bento). You can read more about this at https://8020japanese.com/japanese-word-order/
Duolingo hasn't really taught me about the use of で and に very well, it seems. In a previous question, "I eat luch AT (に) eleven A.M.", at is NOT used as a 'directional' term, as others have suggested. So of course when I come to something like this question, I would put ni instead of de. I think Duolingo needs to better differentiate between these two.