I can only comment in general terms about these sorts of events. I haven't seen the Germany info. Sounds like a fairly routine situation for flight planners, with large sections of an airspace region closed (usually this happens with ATC strikes, or ATC equipment failures, various military exercises, significant weather - this one is of course a short-notice situation - and so on). They will usually plan to fly around the affected airspace, assuming the upper level of the closure prevents them flying over the top.
As an example, a Denmark - Italy flight might (and bear in mind this is simply a general example) choose to file to the west of German airspace and route via the Netherlands, Belgium, Fance / Switzerland, Italy. Or perhaps go east via Poland - Austria - Italy. The advantage being that they can still operate the flight. The disadvantages being the extra distance, fuel burn, time and so on. Also, adjacent FIRs will become more congested during the closure times and might have flow restrictions applied, which adds to the potential for delays.
It's more an inconvenience than a major problem for the airlines; it's something which happens on an extremely regular basis and they are well used to dealing with re-routes. Eurocontrol does a pretty good job of managing these sorts of route disruptions especially when everyone's had plenty of notice to plan for them, and such closures happen regularly and generally unnoticed by the travelling public (save for perhaps an increased wait for pushback on a slot time).
No idea if any airports are located within notified sections of airspace due to close, but they would probably have either pre-approved routes in and out, or individual coordinations with military ATC to ensure they could continue to operate. In practise I'm sure the airspace closure won't cover any major airports, to limit such disruption anyway.