Learn English – What’s the difference between “I see nothing” and “I don’t see anything”

Cutlery has two definitions: 1. cutting/edged implements used for serving or eating food; 2. eating utensils in general. Without further context, an American is likely to assume the first definition (knives), while a Brit is more likely to go for the generic meaning. Silverware also means eating utensils, especially silver-colored ones, though nowadays, most silverware is not actually made of silver. An American synonym that does not imply anything about the silver content (or lack thereof) is flatware.

Crockery is completely different: in British English usage, it means the things on the dinner table that are usually made of china or porcelain -- plates, bowls, saucers, cups, serving bowls, etc. In American English, crockery is used for certain earthenware cooking pots, but given enough context, an American would probably understand crockery used according to the British definition.

Nothing really. In English you tend to get a lot of words that mean the same thing, sometimes there are historical or poetic reasons for choosing one word — but not in this case.

Other than big being a much more common word and large sounding more refined there aren't many areas where you would use one over the other for purely grammatical reasons.
Note that big can also mean "major or important" — so big decision, big spender.