Do you want me to (do something)?

Use this phrase when you're offering to do something that will help the listener or make them happy.

For example:

Do you want me to call a doctor?

Do you want me to leave you alone? 

Do you want me to cook tonight?

 When you use this phrase, you sound like you're offering to do something that will make the listener happy. It doesn't sound like you want to do it for your own enjoyment.

leave (someone) alone

This means to stop bothering someone. With friends and family, it may mean to stop asking questions, or to just give them some quiet time. You may ask a stranger to leave you alone if they are making you uncomfortable. 

This guy at the bar would not leave me alone.

Sometimes I just leave him alone ‘til he’s in a better mood.

We can also say “leave (someone) alone about (something).”

My mother won’t leave me alone about the Christmas party!

This probably means the person’s mother is asking a lot of questions.