Will giving big names for class and id or variable and function result in increase in file size?

Answer 1

More you add the content greater the file size. So ladge names should not be the only reason.
But there are some naming convention guidelines we should follow for better performance.
Search for naming convention with preferred programming language.

Answer 2

In theory yeah, each character you write in a file is worth some bytes, so more character more bytes
But if you're only talk about class or id, its not so much