Translation:I eat inside the restaurant.
I am really not sure about this, but in another discussion it was mentioned that うち stands also for "your in-group", thus what you are referring to may be in this context. Like inside/within a group of people. But I'm only guessing here. It would be great if someone who knows about this could add. :)
Because both particals have different uses. に is used to indicate the goal (レストランに行きます : I go to the restaurant) the same way as へ ; it can be used to indicate a position too, as with あります ; and finally you put it with time such as 7時です.
で is a particle you used to talk about the location when an action is performed. Basically, you were or you are currently in a place and you do something.
I like to compate this type of construction, which is common in Japanese, with the "compound prepositions" of English such as "on top of". If you remember that Japanese have postpositions instead, and that the English "of" changes the order of the genitival phrase compared to the Japanese "no", the underlying structure is actually exactly the same: [[[[headword] + genitive] + spatial relation] + adposition]. It's just that the outward order is reversed in English:
[[[[resutoran] no] naka] de] = in the restaurant's interior
[on [top [of [the table]]]] = on the table's top
Actually, "I am eating" would be the equivalent of 「食べています」as it communicates a current state of action. You are currently eating in a restaurant. 「食べます」on the other hand, communicates the same thing as "I eat" in English. Given the lack of context provided by the surrounding conversation, the best translation of this sentence would be "(I) eat in restaurants".
No, I'm afraid this isn't quite right. When verbs are conjugated like this and 「ます」is appended, it's the equivalent of saying you do this in general (or that you will do this in the future, but in a very polite way. As there is no difference between present perfect polite and future polite in Japanese, this could also mean that you will do it in the future. In this case, 「食べます」is equivalent to "(I, you, etc.) eat" (or "will eat"). To convey that you are currently doing the action, you need to convert the verb into its て-form and append 「います」. In this case that would be 「食べています」, which would translate to "(I am/you are/etc.) eating".
I wrote "We eat in restaurants," but DL said the correct answer is "We eat in a restaurant" with "a restaurant" underscored, indicating my choice for plural restaurants is the problem. I thought the sentence could be interpreted as I/We eat in/inside a restaurant/restaurants. Am I mistaken, and if so, what is my error? Arigato.
を is a transitive particle, as in the action is being performed on the object. i.e. パンを食べます (I eat bread) because you're eating the bread. You wouldn't use を in this sentence because you aren't eating the restaurant, you are eating INSIDE the restaurant.
I'm not as sure about で, but the way I learned it is something like "by means of."