I would like to know which Chinese word is used when we are speaking about the heart as an organ, and not a feeling or the seat of soul affections. The most commonly used word :-)
When referring to the organ in a medical setting, it'll often be the longer, more precise form 心脏, e.g.:
His father has just recovered from heart surgery.
By your description, it looks like you would want to use this longer form.
When used more casually, it'll often be the shorter form 心, e.g.:
His heart gave a sudden leap when he saw her.
This still literally describes his heart jumping, but it could also be used figuratively. Then it gets a bit more metaphorical with e.g.:
She has a kind heart.
It is also often used metaphorically in the construct 心里 to indicate personal feelings, e.g.:
It really breaks my heart to see them this way.