Can I send btc to a totally offline wallet? I want to setup a totally offline armory wallet. is it possible to send btc to a totally offline pc? Is it also safe, I guess it must be synchronized with the whole network, right? And there is something else, armory gives a paper wallet with a long code, can I use this code with any other software, in case something happens to armory?
Yes to both questions. 

You only need a wallet connected to the internet to remove coins from your account, not to add new ones to it. 

A paper wallet can be used with any bitcoin wallet application.