I'm not sure about 'pounding out of my chest' but'my heart was jumping out of my chest''my heart was pounding'are idioms.
meaning a person without no mercy to others and a person that mercy to others.
"With a big heart" means one is sensitive to the needs of others.
To want to have completed a goal.
"Put your heart into it" means to put as much effort as possible into something.
you have broken somone's heart means to hurt someone feelings.
"Take heart" means to be courageous or hopeful, to think positively
The image is of a heavy weight on your heart (which is inside your chest) - you are getting rid of that weight by telling someone why you are unhappy. This idiom means to share your feelings and thus "clear the air" of suppressed emotion.
Unless there is truly something wrong with your heart, then yes, it is an idiom. My heart fell, my heart exploded, my heart sang, my heart doing anything other than pumping blood is an analogy and an idiom.
Faint means weak or not strong. The heart is considered the emotional organ so someone faint at heart would be emotionally weak.
This idiom implies that someone's joy and happiness have vanished completely or abruptly. It suggests a sudden and total loss of positive feelings or emotions.
"To be" is not an idiom - it's a verb.