Good job all the way around...
I found the linguistics interesting. Swiss have regions in a Swiss dialect of each of German, French, and Italian, while ATC language is English. Instructor and Unicom at the grass strip both sounded like German accent on English, Instructor used English, German, and French depending upon who he was talking to. Pilot sounded like UK? and Basel ATC seemed to work a mixture of French and English. I also found it interesting that even while speaking in German and French, English words kept showing up, like they are universally used. Fascinating...
And then doing everything they could to bias the emergency in their favor, using as much time as needed, etc. Good Job.
As to the failure, only the teardown and recovery of the lost pieces will show for sure. Long list of possible sources. The still photo shows no scissors and no brake line hanging, and no sign of a stub of the wheel end of the strut. They landed and departed OK, so the gear was down and rolling, if aimed wrong when they were on the ground, and then it seems to have fallen out after they lifted again.