"I am eating some cheese."
Translation:Ik eet wat kaas.
No. Sommige is half a false friend for English speakers, so to speak. Contrary to some, sommige can only be used in the countable case. And contrary to the restriction of English less to the uncountable case, which was invented out of the blue by prescriptivist pedants and is still not widely adhered to, this restriction of sommige is an actual rule of the Dutch language.
I don't think so. I think if you really want the plural because you are eating several kinds of cheese (or several entire cheeses [edited: this is not proper English but a literal translation of proper Dutch]), you would say "Ik eet sommige kazen." The reason is that in this case you are using an aspect of kaas that makes it a countable noun. Wat is for uncountable nouns and sommige is for countable nouns.
The same thing applies that I wrote earlier concerning "sommige kaas". Sommige and enige are morphologically plurals. They can only be used with plural nouns, not with uncountable nouns. In this sentence, kaas is used as an uncountable noun.
However, in Dutch (and German) it is much more normal than in English to refer to an entire wheel or loaf of cheese simply as "a cheese" and take the plural of that. Hence the following is as grammatical as it is unhealthy:
Ik eet enige kazen. - I am eating quite a few wheels of cheese.
(The same principle applies to bread, again also in German.)