First of all the device preview would only show you the site in a certain resolution (in a frame), nothing more AFAIK. So ti does not change any of the content / layout.

OnMobile sites: there are two ways of doing this.

1. Present the whole site in mobile way to users.
2. Create an extra mobile site and redirect mobile users to that.

AFAIK the module skin that comes with DNN pro is use for version 2.

For option 1, you need a special skin mostly based on something called "responsive design".
That's a skin that changes it's layout based on the device a user uses.

I think there are some options available in the store, but I never tried any of them.
I build skins for clients, I have never bought one...

So this means the mobile skin "only" shows the content in a different manner, there's no auto conversion magic behind the scenes.

There are some solution that can switch to a different skin for mobile devices, but I haven't used them.
(we have our own solutions)

 HTH