First of all, I wouldn't call the Landgericht "district court" - here in NZ, the district court is always the court of the first instance (the bottom level, if you like), and this may also be the case in the UK, whereas the Landgericht is also the appellate court for cases heard before the Amtsgericht in the first instance, and therefore a court of both first and second instance.

I would go for s.th. like "Darmstadt Higher Regional Court (Landgericht Darmstadt)", adding the proper German title in brackets, as the systems don't match exactly.

anorden => has decreed [directed] that preliminary proceedings be held in writing

Termin zur mündlichen Verhandlung = a hearing date has not yet been set [fixed]

zustellen => that this document be served on the third party defendant as soon as possible / that the third party defendant be served with this document as soon as possible (zustellen is not just sending/forwarding)

I'm using the subjunctive, because that is the more polite form of addressing the Court.