Translation of Hoffnungsschimmer

There is a small misunderstanding about the homework. I can do them, but they will be too confusing? I am trying to find the article from where I took the sentences in order to ease the task for all students.
Well, you're already here ... would you ever have thought that I'm a member in facebook? You are a funny guy. What else is happening? Did you already settle down in your new country of choice?
I wish you a safe journey. In what city will you be staying in Germany? We want to buy a small flat in Eastern Germany. And if everything goes well, we want to build a small house next year.