"She is very hungry."
Translation:Sie hat großen Hunger.
in this case the adj Gross, is declined as Grossen, because is the third case (non predicative adjective with no articles), masc. sing., accusative.
The third case is as follow (Masc, Fem, Neut, Pl):
Nominative: M) ...-er F) ...-e N) ...-es PL)...-e
Accusative: M) ...-en F) ...-e N) ...-es PL) ...-e
Dative: M) ...-em F) ...-er N) ...-em PL) ...-en
I hope it helps, Tschuss
Because "sehr" modifies adjectives, as "very" does it in english. You'd say "It is a very big cat", but there's no way to use "very" to modify "cat". Instead, for nouns you use "many/much" in english, which are translated to "viel" in german. So, you'd say "I have many cats". I think that should clarify your doubts! :)
Because you can't use indefinite articles (i.e. ein/eine/einer/eines/einen/einem) with uncountable nouns. So, you can't use "einen" since hunger is an uncountable noun. You are hungry or you are not, but you can't have "one hunger", "two hungers", etc. It's awkard to say that since you can't count "hunger".
Does the verb haben takes always the akk
Yes. Just like pretty much all transitive verbs (those that take a direct object).
and seinen the nominative?
The infinitive is sein. And yes, it has the nominative case on both sides -- both the subject and the predicate are in the nominative case. werden (to become) is similar.