I'm pretty they can be used to show hesitation in fiction or informal writing. But I'm also pretty sure there is some other name for them when used this way.
*I'm probably wrong though*

No, ellipses or '...' when I use them are like a pause or a continuance with dramatics added.

He went to look in the cellar... But Aaron was nowhere to be found.

It's mostly used for pauses, but has to preserve the momentum of the previous thought.