"I am eating soup."
it's not "zupa" because it's accusative case and the verb "jem" is doing something to the noun "zupa".
Nope, he said "zupę". Maybe you're still insensitive for subtle differences. :)
How would I say "I am eating tomato soup?" Is it like italian where you say tomato after soup?
Jem zupę pomidorową.
The noun precedes the adjective here, because pomidorowa is not a secondary or temporal property, but a classifier.
That's interesting. In Russian, it can go either way. The more common version is
Ja jem tomatnyj sup. because tomatnyj sup goes together as one noun.
However, if you say Ja jem sup tomatnyj, then you are emphasizing the type of soup. This emphasis is not usually necessary.