Well the order for the first five channels on the EPG
usually goes: Das Erste, ZDF, RTL, Sat1, ProSieben
But, because Germany does not have fixed mandated EPG system like the UK, everybody basically just does as he likes. From what I've seen after the big five most people have like the first wave of multichannels, like VOX, RTL2 or KabelEins and now also One (ARD) and zdf_neo, then the regional 3rd channels as one big block starting with their own local one.
The cooperation between ARD and ZDF still, especially in the daytime, stems from the time when it was deemed that not enough people are watching at this time of day to warrant two seperate programs. Nowdays they share resources mostly on the basis of cost cutting, or at least trying to look like they are cost cutting. At recent bigger events, like the World Cup or the Olympics, they also started to share studio facilities, even when they are hosting from Germany, like they did at the last Olympics and World Cup. With one central "Olympic-Studio" or "World Cup Studio" they both share, only on screen personell is changed. Which I think is a shame because ZDF especially was known for their huge outside broadcast studios for the WC or Euros. Like in 2008 when they turned the Festspielhaus Bregenz in Austria, that huge open air opera house where they also shot 007 Quantum of Solace, into their studio.
ARD nd ZDF also run a few TV channels in cooperation. Like Phoenix (news), Kika (children, basically CBBC), arte (culture, together with France) and 3sat (culture, together with Austria and Switzerland). Also their new youth orientet online offering Funk is also run by both of them together.
They both have a "we against the rest" image and are commonly refered to as "Die öffentlich-rechlichen" (after their corporate form) or short "Die Öffentlichen" ("The publics") and are often thought of as one entity by the public.