"Caesar" salad was first concocted in Mexico by a chef named César (pronounced Says'-are).

Both the OED and Merriam Webster's give barbeque three syllables. The word is not French. Some people credit it to the New World Spanish word, barbacoa (a framework for supporting meat over a fire) but originally the word was probably Caribbean Indian. An early example from the OED suggests this:
Hickeringill, "Jamaica," 1661- "Some are slain, and their flesh forthwith Barbecu'd and eaten." Adair, 1775, "American Indians," spelled it the way we do, barbecue.

As for Worse ter sauce, most of us over here use Heinz.

I suppose Big Pink would pronounces niche "neesh," in the English Quebec-Ottawa dialect. Cotgrave introduced the word to English in his dictionary or 1611, using Italian nicchia as the root word. His friend Jonson used it in a play three years later, and it has been nitch ever since.