Learn Farsi: این چیز بزرگ است.

chiz is a regular noun meaning "thing". Because we are saying "this thing" (in chiz), we are pointing to a specific item. You add the -i ending to make the indefinite pronoun chizi when you want to talk about "something" or "anything" in general, without pointing to a specific object.

If I wanted to use the new word chizi to say "Is something big?", how would that look?

You would drop the word in (this), because chizi already means an unspecified "something". You would simply say chizi bozorg ast? (Is something big?).

Usually adjectives connect to nouns with an "e" sound. Why isn't it in chiz-e bozorg?

In Farsi, when you use "is" (ast) to describe a noun, the adjective doesn't attach directly to the noun with that "e" sound (which is called the ezafe). The structure is simply Subject + Adjective + Is (in chiz + bozorg + ast). You only use the connecting "e" for descriptive phrases like "this big thing" (in chiz-e bozorg).

How would this sentence sound in everyday spoken Farsi?