This is a metaphor for falling in love.
A 'beating heart' is not a metaphor, but is rather personification.
metaphor
No
Yes, the phrase "his mouth was a vacuum cleaner" is a metaphor. It is used to convey that someone is eating or speaking voraciously or loudly, likening their mouth to a vacuum cleaner.
cold heart
Simile
A metaphor assigns an action to words or ideas, but it isn't literal. The water was so refreshing it made my mouth jump for joy. In the sentence, your mouth jumping for joy is a metaphor.
no the heart is not connected to the mouth .
metaphor just because
your heart is a black hole. your heart is the the sun.
is this phrase my heart is heavy a metaphor