Lets say you have a server where A is the card in the root of the server and B, C, & D are all installed pieces of ice.

A B C D

You want to install piece of ice E in the server, and you've decided that ice C is not living up to what you expected of it and want to trash it. Can you put Ice E where ice C was so that it looks like...

A B E D

I could have sworn that you can but I can only see in the rulebook where it says that you can trash something and put the new one on the outside. So that the only configuration would be

A B D E

Thanx in advance!

The second is correct. The only way to install something NOT in the outermost position is through card effects (such as Midori).

Tenma Line can't get here fast enough.

Lets say you have a server where A is the card in the root of the server and B, C, & D are all installed pieces of ice.

A B C D

You want to install piece of ice E in the server, and you've decided that ice C is not living up to what you expected of it and want to trash it. Can you put Ice E where ice C was so that it looks like...

A B E D

I could have sworn that you can but I can only see in the rulebook where it says that you can trash something and put the new one on the outside. So that the only configuration would be

A B D E

Thanx in advance!

This is most likely just a translation issue but the root of the server is specific to central servers (that's where cards go). For remote servers you simply install cards (assets, upgrades and agendas) in the servers.