The meaning of surprise are :
The astonishment you feel when something totally unexpected happens to you, or
The state of being surprised,or taken unawares,by some act or event which could not reasonably be foreseen.

The meaning of disbelief are :
A state of the mind in which one is fully persuaded that an opinion, assertion or doctrine is not true.
Denial of belief.

Ways to say it :

Expressing being surprised :
Telling surprising news :
Guest what!
Surprise!
I’ve got news for you.
Do you know what?
You won’t believe it!

Responding to believe or not :
Oh, no. That’s not true.
You don’t say.
Really? That sounds interesting.
Really? It’s surprising that….
Seeing is believing.
Good heavens.
My goodness!
This is really a surprise

The expressions used to say believe or not believe are :
Asking if you believe or not :
Do you believe it?
Wouldn’t you believe it?
Can you imagine that?
You don’t believe it, do you?
Don’t you think it’s odd that …?

Responding to believe or not :
No, I don’t believe it.
Are you serious?
Are you joking?
Are you kidding?
You must be joking/kidding!
Oh, no! That’s not true!
You don’t say!
Seeing is believing.