This idiom or expression has to do with:

Listening to someone’s side of the story.
Listening to all of what someone has to say.

When someone says “Hear me out,” they could mean any of the following:

Let me finish.
Listen to what I have to say.
Let me tell you my side of the story. Etc.

This idiom or expression means:

Paying attention.
Giving importance.

She doesn’t seem to give two winks about what I think.

I don’t really give two winks to whether you are on time or not.

This idiom or expression has to do with:

Having a lot to hear.

Used in a positive way:
Great speakers at the meeting today! We sure got an earful.

Used in a negative way:
Stop it! I’ve got an earful. Go lecture someone else.

This idiom or expression like sentence means:

I’m listening.
Tell us about it.
Tell me about it.