Extrude edge along roof angle I'm trying to extend an edge from the existing roof face axis. 
How can I do this? I want it to go all the way down to the lower part of the building. It must connect there (I want a edge there too so the remaining right part of that lower building will be cut off).
You can create new transform orientation for that edge.

Select side face of the roof. In the N panel create new transform orientation (you can create it pressing Ctrl + Alt + Space, as Gonzou mentioned):



The created orientation should be selected as active. If it isn't, in Alt+Space menu select this orientation (it will be called something like Face). Switch to Edge selection mode, select your edge, extrude it, cancel moving by Esc and start grabbing pressing G twice.