"Dumneata mănânci" - second person singular, the same as "Tu mănânci"
"Dumneavoastră mâncați" - second person plural, the same as "Voi mâncați".
"Dumneata" is the formal version of "tu" and should be used when addressing a younger person.
"Dumneavoastră" is the formal version of both "tu" and "voi". It differs from "dumneata" when adressing one person, in that the person is supposed to be older or of the same age as yourself.
No, but you can conjugate the verb in the second person plural and it can mean that you are adressing people in a polite way (if you omit the pronoun). It can also, however, mean, that you are adressing more people that you know well (a.k.a not necesarilly in a polite manner). Example:
Voi mergeți la restaurant? (adressing more people in a non-formal way)
Dumneavoastră mergeți la restaurant? (adressing one or more people in a formal way)
Mergeți la restaurant? (it can have both the meaning of the first and of the second sentence, depeding on the context)
The third form is perhaps the easiest to use and it is also the most common.
Voi is the plural form of you, but can also be used as formal. If talking to one child, you say "tu esti," two children "voi sunteti," and to an adult, you can use either vow or dumneavoastra. Either way, voi is officially you all, but we translate to English as you, because we have no plural form for the word.