So basically Knight hosting ability can be worded as "skip an ice before and after to host on", is it correct?

Can Knight host on the ice beside the server?

You can move it from its current host ice to any other installed piece of ice (including those protecting other servers), just not on the ones directly in front or behind the current host ice.

Sounds about right. Vertical movement needs at least one space. Horizontal movement looks absolutely fine.

it seems that the verticle movement might occur a debate

What debate? ICE protecting another server is not directly before or after the host ICE.