why are emotions felt in the chest?

This is due the effect of the neurochemical changes which occurr in your brain during depression (which is essentially what heart ache is) and how they alter the physiology of your body (anxiety can cause palpitations and an adrenergic effect, lack of parasymptahetic tone, etc.).

Without getting too technical though I'll say this - almost everything you experience in your body is regulated by your brain. People have this weird idea that the brain and the body are separate, when in reality they could not be more the same.

This is mostly confirmation/observer bias. Essentially, you feel pain there because you were taught that it was called a "broken heart," and you assume that your heart must suffer for it. The idea of attributing emotions to organs was documented in ancient Greco-Roman texts, and probably occurred before then. This is likely because adrenaline and other hormones have a visible impact on the heart. However, all emotions originate in the brain and have the majority of their effects there.

Emotions are indeed felt in the body. I am not sure there needs to be a reason - maybe you should look into evolutionary biology, or the physiology of emotions.

I don't know if this is a good source for info:

http://www.slideshare.net/shaan_47/physiology-of-e...

Hmm... Good question. I think that emotions are in our brains, but the reaction they cause to our bodies is what we feel. Like if someone falls in love, that emotion causes excitement which causes the heart to beat faster that gives us the feeling like we feel love.