'Franistek has already lived there for a year or two' should be an accepted answer.
Nope. His name is František, not Franistek.
"František is already living there ..." is not accepted. Is this an English idiom issue?
To my native AmE ear, "IS already living there for a year or two" sounds wrong. I'm fairly sure that "has been" is what's needed here, since it takes care of both his past and current "living."
I think it is not correct with the time interval, but I may be wrong. But it does exist on its own.
The word order of this sentence is crazy. How am I supposed to ever be able to construct a sentence?
There is a lot of freedom here, just keep "už" and "tam" second position, start with František, and then it will be hard to construct anything wrong.
English does not need 'already' to say 'has been'. (It reminds me of how déjà works in french.) This is discussed somewhere else.
Already is not necessary. If your answer was not accepted, use the report button.
Why is it wrong "František has been living there for a year or two years already." ?
It's not necessary to repeat the word year, it's redundant.
As a native English speaker I would accept "is living" as well as "has been living", particularly if he is still living there. A similar construction is used in French and German
See the previous answer by Bonehead Bass. French or German are completely irrelevant.