I know it's possible. I say that because I've done it before through some sort of discount at my work. After purchasing online, I get sent a link in my email to download and install.
No, but it can be installed over a local network if you have another Mac with an optical drive.
http://www.microsoft.com/mac/office-2011-digital-downloadIf you buy it on disc it offers you a digital download option for Air like computers.