It means that someone was very sick, but they recovered after a long battle with illness.
If your plans fall through, it means they did not work out.
This is not an idiom. An idiom is an expression whose meaning cannot be deduced from its elements. To go through fire and water for someone is easily understood to mean to make a special effort and to undergo difficulties for that person's sake.
To seek a favor from someone through flattery
If you slept through something, you did not wake up in time to attend it; you slept until after the event was over.
A dog sled idiom is a sled that men go on to get pulled by huskies
It is sometimes said that if you deceive someone you have pulled the wool over their eyes.
It's not really an idiom. It means "what are you thinking about."
RFP is not an idiom. It's an abbreviation.
It is not an idiom, it means your nose is itching.
It's not an idiom. It means the tip of your nostril.
idiom means expression like a page in a book
"Sieve" is not an idiom. See the related link.