#3-Q: Is there any rule governing the use of "big" and "large"?

A: Yes.
When you use a ditionary to find the define of "Big" and "Large", you may confuse about how diffirent they are, they both describes by each other.But, through searching corpora, you can know how to use them better.

"Big"

• is often used to describe the shape of an object.
  => big car, big house, big TV, etc.
• sometimes to emphasize the important of things
  => a big difference, the big challenges

"Large"

• is often used to describe the amount of objects.
  => large number of books, large quantity of documents, large sums of money, large classes, etc.
• usually used in standard things.
  => large coke, large fries