Hi,
1. Dating is a time to learn more about someone. Many people make the mistake of giving away their hearts too easily.
- "give away their hearts too easily" means "reveal things about them too easily", right?
It's true that 'to give something away' can mean 'to reveal something', eg He gave away the secret.
However, 'to give away your heart' usually means 'to give someone all your love', and that seems to be the meaning here.
2. Be wary of someone who wants to cut you off from your friends or family.
- "cut you off from" means "separate you from", right? Yes.
Best wishes, Clive