'ci' translates roughly to "us" in this context.. vediamo is understood that you (the person and I am going to see) and I are the "we" who will see eachother tomorrow. Although I guess it would work for a group of people as well but "we see you tomorrow" is a pretty awkward way of saying that. Maybe a native Italian speaker will come along and tell us if 'ci vediamo' is used for groups as well as for two individuals. For instance, how would you close a meeting that will meet again tomorrow..
Shall implies futurity (determination, promise, or prophecy); will implies volition. There are subtle differences between when you use 'will' and 'shall,' and it's by no means accurate to say that 'will' is not first-person singular and plural in English - especially since every single native-speaker of English uses 'will' thousands of times a day to indicate a desire or plan to do a thing. We use 'shall' when we wish to say a bit more forcefully that something absolutely is going to happen. We use 'will' when we want to say a bit more forcefully that it's my desire and intention to do a thing.
Child: I will NOT go to bed! Parent: You SHALL go to bed - and right now!
It's a 'rule' almost not followed at all nowadays, certainly in ordinary speech, but here's Strunk and White (notice they are talking about formal writing, not spoken English - despite having as an example an apparently drowning person using formal written speech to invoke assistance): "Shall, Will. In formal writing, the future tense requires shall for the first person, will for the second and third. The formula to express the speaker's belief regarding a future action or state is I shall; I will expresses determination or consent. A swimmer in distress cries, "I shall drown; no one will save me!" A suicide puts it the other way: "I will drown; no one shall save me!" In relaxed speech, however, the words shall and will are seldom used precisely; our ear guides us or fails to guide us, as the case may be, and we are quite likely to drown when we want to survive and survive when we want to drown."
"Shall" isn't a different conjugation of "Will", As you seem to be making it out to be, But rather a completely different would, Albeit with similar meaning. I feel it should work here, But so should "Will", Neither is more correct then the other, There are simply slightly different meanings.
"chi" is pronounced "key", "ci" is pronounced "chee". Italian is the opposite of English in this regard. The addition of the 'h' in Italian means the 'c' sound should be pronounced as a hard consonant.
"conchiglie" (pasta shells) is pronounced "con-keel-li-ay". "zucchero" (sugar) sounds like "zoo-ker-o". "cibo" (food) is pronounced "chee-bo". "cena" (dinner) is pronounced "chey-na". "ciao" (hello/bye) - sounds like "che-ow".
This short video explains it nicely: https://www.youtube.com/watch?v=ueia5n1LvY8
"Ci Vediamo", Literally "We see ourselves", Has been translated in other exercises to "(I'll) See You!", Which makes sense to me, But begs the question, Why isn't "See you tomorrow?" accepted here? Especially because in English "We're seeing eachother" would general be understood to mean "We're dating", Atleast where I come from, Which I don't feel is the intended meaning of this sentence.
He might be referring to statements like, 'Boy, is it hot' which is grammatically a question (Is it hot, boy?) but is not really asking for information, but making a statement: it is hot. I'm just guessing, since in English, a question mark does indicate a question (at least as far as I can think of any examples) and the 'question' I just used as an example would not have a question mark, but an exclamation mark (Boy, is it hot!). There can be statements like, 'You're not going?' which while a statement, use intonation (in speech) or a question mark (in writing) to indicate that it's functioning as a question. But certainly as it's written, formaggiamente's remark is not true.
A statement with a question mark IS a question, Just not a normal sort of question, For example "We shall see eachother tomorrow?" implies it's established that we shall see eachother tomorrow, But the speaker is shocked by this information, And thus is asking to confirm it, While "Will we see eachother tomorrow?" simply implies the speaker does not know if we will see eachother tomorrow, And thus is asking to find out.
"See" is a Transitive Verb, I.E. it requires an object, And obviously "Tomorrow" can't be the object as it's a period of time, Not something you can see, In some contexts you could use it without an object, If it's evident what would be seen by context, E.G. "What do you think is behind that door?" "I don't know, Shall we see?", But in most cases you'd need a direct object, Such as "Eachother".