Can "už" be placed at the end of the sentence?
No. Not at the end of this sentence.
What kind of sentence that it can be placed at the end and what kind of sentence it can be put at top?
I do not understand "at top".
But there are these examples:
Bude to už? Will it be finished/ready (already)?
Ticho už! Be silent (already)!
Ale už! disagreement, if you want to stop someones continuing misbehaving
Haha, can you think of a way the ale už makes sense for non natives? And I think the op meant at the beginning by at top. Why isn't už in the second position in this sentence?
It can be at the front quite normally. It is a common position for Už.
Why is "gauč" not accepted as a correct answer?
But it is accepted. What was your whole answer?
EDIT: Ok, I can see a report from the time you posted your comment. You wrote: "Už potřebujeme novou gauč." That's incorrect because "gauč" is masculine.