When can corp trash its own ice?
No, ice can only be trashed when installing other ice. 

The terms "in a server" and "protecting a server" are not interchangeable, but rather used discretely to refer to different types of cards and their relation to servers. Agendas, assets, and upgrades are installed in servers, while ice is always referred to as protecting a server, and is never considered to be in a server for the purposes of any rules or card effects.