Why is coś nominative but ważnego genitive? Is the word "important" not being used as an adjective for "something"?
"Coś" generally connects with adjectives in Genitive. Even if it can seem weird, it's just like that. On the other hand, "ktoś" doesn't work in such a way so the form of an adjective always matches the form of "ktoś".
= "It is something of importance".
Is "To jest czymś ważnego" also correct?
To jest is followed by the nominative case, with coś modifying the adjective to look like it's taking the genitive.
If you get rid of the dummy pronoun to, everything will take the instrumental case: On jest kimś ważnym.
Sorry, I didn't understand whether "To jest czymś ważnego" was correct or incorrect. Tks.
It's incorrect; from above, "To jest is followed by the Nominative case"; however, "czymś" is Instrumental and Locative (not Nominative).
BTW. Take a look at https://en.wiktionary.org/wiki/co%C5%9B#Polish for the full declension of "coś".
What would this mean: To coś ważne.
Well... in a way, the same, and in a way, nothing. The message should be understood, but it's just not grammatically correct.