The sentences where you leave the pronouns out are pretty annoying and don't really serve a purpose other than to frustrate the user without devoting an explanation to it (I have yet to run into one, any way)
I had a feeling that would be the case and it is probably because I always end my language courses with a "strengthen skills" which must throw in courses I haven't had yet.
Still here. Can someone confirm this:
No personal pronoun because you can leave it out with "want" (like "may")
Bowl is in accusative because it is the direct object of the verb want.
Soup and rice are in the genitive because it is a quantity of these (a "bowl" amount. Like a "cup" amount of tea.)