As a native speaker of Ukrainian I almost never use чи unless I want to sound really formal/polite.
"Чи не бажаєте ви випити чашку кави?" - "Would you drink a cup of coffee?" sounds natural and formal.
"Чи вони грають у хокей?" - "Do they play hockey" - sounds okayish, but a bit weird if I speak to a friend. Might be regional though. I'm from Kyiv.
As I understand it, Ukrainian doesn't have the verb forms we have in English, so you would have to go by context and intonation. Sort of like the чи that started this thread: they don't use it because intonation and context make it clear that it's a question. But English speakers like to put it in because that's how our language works.
<rant>And гокей seems like a lost cause. Even though it is lifted from an English word, that starts with the Latin letter H there seems to be an insistence on turning it into Cyrillic Х despite the availability of the actual phonetic transliteration (Г). One could argue that "that's just what it is in Ukrainian" -- but then Ukrainians learn English and insist that NYC has a borough named "Manchattan!" </rant>