"Having a heart" means to show compassion. It can also mean to show mercy, generosity, or forgiveness.
Example:
"Show us you have a heart and donate to our animal rescue organization!"
Weak hearted or almost having a cowardly heart.
meaning a person without no mercy to others and a person that mercy to others.
The idiom "my heart was in my mouth" means feeling extremely anxious or nervous to the point where it feels like your heart is pounding heavily in your chest.
To want to have completed a goal.
"With a big heart" means one is sensitive to the needs of others.
"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
You have 10 hearts with 2 health per heart, meaning a maximum health of 20
crave your name on hearts not on marble
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.
"To be" is not an idiom - it's a verb.