They said in episode 1 that Stamm was an orphan - his parents had been killed in a car crash. Presumably he'd have had some other family and friends though.

I guess the Stasi could have used an agent to pose as a West German official, and tell the real Stamm's parents that he was involved in a hush-hush operation for a few weeks and therefore should not be contacted.

Didn't the boy have parents who would want him to visit? Or did they deliberately choose an orphan?

More to the point, what happened to the friends and relations of the real Moritz Stamm?
Wouldn't they get suspicious that he didn't visit, write, telephone etc?

If you rewatch the sequence it a car is following the train I assume the assassin pushed the young solider's body out the window to the waiting car.

Good question, because clearly no one could know he was actually dead. I would imagine they lugged him out, confiscated all his stuff and disposed of the body somewhere. But to get close to an enlisted man, that's probably as good a place as any??