does ''don't know'' also mean ''not sure''?

Yes.

"I don't know" can mean "I'm not sure."

It can mean "I have no idea" or it can mean "I don't know for sure."

It can even mean "I disagree with you."

Examples:

> I don't know which one is harder -- algebra or geometry.

(This means "I have no idea.")

> My friend said that geometry is harder than algebra, but I don't know if that is true or not.

(This means "I am not sure.")

> My brother thinks that algebra is harder than geometry, but I don't know about that. I passed algebra without any trouble.

(This means "I disagree with my brother.")

People often use them to mean the same.

Personally, I take "I'm not sure" to mean you have *some* idea of an answer; but "I don't know" to mean you have no idea at all.

And people often use "I'm not sure" to pretend they have some idea in mind, so they won't look too uncool, when they really ought to admit they don't know.

It depends. Sometimes I say I don't know when I really do know and I don't want to say. But to answer your question, I think they are the same thing, yes.

What if Selena Gomez or Robert Pattinson asked a person out on a date and the person said "I'm not sure." Well, don't you think if they were interested, they would instantly say "Yes"?

"Don't know" means low interest.

Yes, if one is unsure about something, then it is fully consistent to phrase it as "don't know".

It depends on the context

if its something factual it could mean both dont know and not sure

in terms of dating it is a clear no im not interested

Well to be honest, it depends on the situation and how you use the term.