"You eat that much meat!"
Translation:Vi manĝas tiom da viando!
why doesn't viando end in n
Because it's after "da" - objects of prepositions are generally in the nominative case.
Because you are measuring the quantity of meat.
As a first approximation, you could simply learn "kiom da" together, much as "because of" often appears together in English (why do we say "He arrived wet because of the rain" and not "He arrived wet because the rain"?).