They're both considered figures of speech and they both liven up writing. Other than that, they're not very similar.
It is actually an idiom.
Idiom
No, "blew his top" is considered an idiom.
Hyperbole
"Life is just a bowl of cherries" is a popular idiom that at one point was made into a song. It simply means that life is good and everything is going great!
In fact, no, feeling blue is not a hyperbole, it's more of a metaphor. A hyperbole is a exaggeration.
It is just an exaggerated way of saying something happens quite often - it is hyperbole, not an idiom.
No. Hyperbole is an exaggeration. I was so cold last night that my nose turned into an icicle and dropped off. An idiom is any combination of words in a language where the meaning is not quite what you might expect. When Dubya tried to talk French the way he didn't know how to pronounce 'r' stuck out a mile. 'Stuck out a mile' just means 'was very obvious'.
What you are referring to is a Hyperbole, or an extreme exaggeration. It usually means a feeling of sadness, but your heart is not literally sore. It could also be an idiom, as in "Heartache", which has about the same meaning.
Yes, its an idiom because it's a saying. It might also be either a hyperbole(an exaggeration) or a metaphor(a comparison between two things without using like, as, or than).
Exaggeration is a pretty good synonym for hyperbole.
No, it is an idiom because you can't tell what it means by trying to define it literally. Hyperbole is exaggeration - an example would be "It was raining so much we had to row a boat to work."