It's not an idiom because you can easily figure out what it means. If you do something "at any cost," then you don't care what happens or who gets hurt.
It means "I can't take any more."
It means that you can be easily be woken up by any small sound.
This is not an idiom - it means exactly what it says. You will use any means to achieve your goal.
Body is a word -- it can't be an idiom. You can find many meanings for this word in any good online dictionary.
It's not an idiom because you can easily figure out what it means. If you do something "at any cost," then you don't care what happens or who gets hurt.
The idiom "to read at any cost" means to be willing to do whatever it takes to read or access something, regardless of obstacles, challenges, or difficulties. It emphasizes the strong desire or determination to obtain and engage with written material.
It means just what it sounds like - no matter what the cost, do it.
A "crash course" is a very fast lesson. This usually means that someone learns something without any real training, through trial and error or experience.
Idiomatic expressions are phrases or sayings that have a meaning different from the literal interpretation of the individual words. They rely on cultural, historical, or metaphorical associations to convey their intended meaning in a concise and familiar way. People use idiomatic expressions to add color, emphasis, or clarity to their communication.
Are you asking if this expression would be acceptable in formal English? It may not be the worst usage in formal English, but I would look for another way to say it. It is idiomatic, and may not give a consistent meaning to any reading expecting standard usage.
"Beg" is not an idiom. An idiom is a phrase that you cannot understand unless you know the definition. "Beg" is a word that you can look up in any dictionary.
Variable is any letter used in an algebraic expression, and can vary (change form) to be any number, and one variable means the same number in any single algebraic expression. Usually algebra is simplifying the expression or equation until you know what the variable is equal to.