Kiev from a Russian pronunciation Киев (Russian) http://forvo.com/word/%D0%BA%D0%B8%D0%B5%D0%B2/#ru
Kyiv from an Ukrainian pronunciation Київ (Ukrainian) http://forvo.com/word/%D0%BA%D0%B8%D1%97%D0%B2/#uk
I'm very sorry, only "Kyiv" is accepted according to the politics of the UkrDuo administrators.
Kiev is a common way to spell Київ in many languages.
My personal opinion is that it doesn't make sense to forbid it, since in many sources it is still officially spelled like that. Maybe their idea is that if we spell Київ differently, it will change people's attitude to our country. Which I think is not true. People can spell it any way they want, and perceive Ukraine as an independent country; and conversely they can be forced to spell "Kyiv" only and still treat Ukraine the way they want. It's not a subconscious effect on the mind or something.
Besides, what city is spelled and/or pronounced in a foreign language exactly the way it is in the original one? "Roma" is "Rome", "München" is Munich. Apart from that, "Kyiv" is confusing, it's unclear how to pronounce it. Since foreigners can't usually pronounce "и" anyway, and don't know that "y" means "и", spelling "Kiev" only makes sense. The short "i" in English sounds similar to "и", actually.
But... I'm not the one deciding.
I don't really mind. If I'm getting a political-schooling from Duolingo about how the name should be spelled according to post-independence, I'm fine with it. The thing is, Kiev might be out, but in English "Kyiv" doesn't really match the pronunciation. Why wouldn't it actually be "Kiyv"? That or just stick with what we've been spelling in English all along: Kiev.
Rent for 1-bedroom is from 4 000 UAH/$150 (you don't want to live in those) to 6 500 UAH/$240 (these are generally OK if close to subway station or nice if far from it) to 8 500+ UAH/$315 (really nice ones)
Well, yeah. But here average monthly salary is 7 886 UAH ($300) in Kyiv and 4 585 UAH ($175) in Ukraine after tax.
Oh, of course. I didn't take that into consideration in my last comment. Sorry about that.
Please add "Kiev" as an acceptable translation. This isn't a political course. Please focus on the grammar.
I fully agree with you that politics should stay out of this. However, the original author of the course and two other contributors have agreed on removing "Kiev" and removed it.
Please read my comment above for my own opinion... I'm a contributor at the moment, but wasn't participating in the decision when it was made.