"I eat inside the restaurant."
I'm afraid I don't understand. Why is the particle で used here, instead of the particle に? Do they not both indicate position (e.g. ...間にいます)? I've looked it up online, but I can't find a satisfactory explanation. Is this just one of those things that you need to memorize for every situation?
の is a possessive particle, 中 is inside. レストランの中 can be thought of as "the restaurant's inside". You wouldn't use "the restaurant's inside" in English, but in Japanese, when you want to say you did something somewhere, you use で.
The same is with の隣(next to), の前(in front of), の後ろ(behind), etc.
You've got the possessive (の) the wrong way around. 「中のレストラン」 would be like, "The inside's restaurant". Conversely, "The restaurant's inside / in the restaurant" would be, 「レストランの中」as it was in the suggested translation.
Additionally, 「食べでいます」is not the right form for this question. It looks like you're trying to use te-form/て-form, which would be a continuous action, so, "I'm eating inside the restaurant", rather than just the "non-past / polite" masu-form/ます-form, 「食べます」. Also, the て-form for 食べる isn't 食べでいる, it's 食べている; or in ます-form, 「食べています」You can tell how to conjugate into て-form based on the character the root word ends with, but that'll take practice (and probably a lot of wrote memorisation). E.g. 食べる becomes 食べて, and 飲む (のむ [to drink]) becomes 飲んで.
Finally, が isn't the particle you want here, as it would serve to connect the verb "to eat" to the noun "restaurant", but not in the way you expect. Firstly, in both cases "I will eat at the restaurant" & "I am eating at the restaurant", the subject is "I (as in me)", so we could prepend 「私は...」to the beginning of the Japanese sentence without fundamentally changing it's meaning. However,「私はレストランをたべます」would mean, "I will eat (a) restaurant(s)". If you used が, it would largely mean the same thing, except I think the sentence would actually also be incorrect as 食べる is exclusively "transitive" (needs a direct object via を). This is why で is used in the example sentence, it shows "where" the action of eating is taking place, but not "what's" being eaten.
Putting all of that together, 「(私は)レストラン(の中)で食べます」would be valid and mean "(As for me), I eat (inside) [at] the restaurant" or in て-form: 「私はレストランの中で食べています」"(As for me), I'm eating (inside) [at] the restaurant." In both cases, 「私は」and「の中」are both fine, but contextually unnecessary.
Have a read of this; I'd recommend perusing the whole site as it's a really valuable free resource: http://www.guidetojapanese.org/learn/grammar/verbparticles#The_contextual_particle
If it's part of a combination with other Kanji, it's always read ちゅう (or じゅう), but the standalone version (like here) can be read either なか or ちゅう and you simply have to figure out which one it is based on the context of the sentence and experience. In this example, it's referring to the inside of something, so it's なか.
As a general rule (but there are exceptions), if you're using it for the English words "inside/in", choosing one "among/within" a group, or talking about the "middle/center" of something, it's なか, and otherwise it's ちゅう (or じゅう).
(And all this isn't even mentioning that technically it has 2 other readings, too, although people tend to use a different Kanji or no Kanji at all for those words.)
You would use the particle 「で」instead of 「に」because the で particle is used to describe where the action takes place, whilst に is used to describe what place you are in. https://www.wasabi-jpn.com/japanese-grammar/japanese-particle-ni-clear-up-all-doubts-you-may-have/#1 has a good explanation on this.