"han äter en soppa" or "han äter soppa?"
Does Swedish require the use of an indefinite or definite article with a noun, regardless of the context? With some sentences this is fine, but I can see it changing the meaning with others:
"Han äter en kyckling" implies he's eating an ENTIRE chicken, as opposed to "Han äter kyckling" which suggests that he's just eating chicken, with no information about how much.
No Swedish does not require the use of an indefinite article with a noun nor the use of the definite form of the noun. In some cases you need to use the plural form of the noun if you leave out the article, in other cases the singular form works as a collective without the indefinite article.
The discussion in this thread might be worth reading.
Example of words that I believe always will go in their plural form unless an indefinite article or definite form are used together with äta: makaroner, ärtor, oliver, druvor and bönor*. All these are quite small and you would normally eat more than one. It might be because of that I would find it strange to use a sentence such as "Jag äter ärta" strange.
I'm in doubt about räkor and kräftor. They are usually used in plural form, but I think it would be fine to use the singular form. The singular form of kräfta is for sure used together with the verb fiskar.
It depends on whether it's a mass noun or a countable, and on context, as you said. Jag dricker kaffe can mean quite a few different things; jag drycker ett kopp kaffe means you are drinking a single cup of coffee.
It can also depend on whether it is a mass or countable noun, but that comes more into play with the words mycket and många. Jag drycker mycket kaffe, but jag äter många kex.