*) What is the meaning of lief rüber in "Ich legte dort die Kasette ein und lief rüber,"?
*) What does "Soldaten sollen die XX misshandelt haben," mean? What grammar rule is this called? How is this sentence different from "Die Soldaten hätten die XX misshandelt haben,"?
*) What is the difference between:
"Dann wäre nach Meinung von Organisationen ein wichtiger Schritt getan," and "Dann würde nach Meinung von Organisationen ein wichtiger Schritt getan worden sein,"?
1 - rüberlaufen - to run over or to walk over (to a place that is a bit away from where you were before, towards another place that is obvious from context).
2 - soll indicates that this is hearsay and that the person who said that sentence is not asserting the truth of the statement. Soldaten sollen die XX misshandelt haben. "And, supposedly / from what I've heard / from what the article I read says, the soldiers mistreated the XX."
Die Soldaten hätten die XX mishandelt haben makes no sense to me.
Die Soldaten hätten die XX mishandelt could either be conditional ("The soldiers would have mistreated the XX [if ...]") or past subjunctive, using the subjunctive in a similar usage of explicitly reporting speech, i.e. "Supposedly, the soldiers mistreated the XX".
3 - a bit like "would be done" and "would have been done".