"Do you have training on Monday?"
Translation:У вас є тренування у понеділок?
And "У + є" is certainly not colloquial. A russism? Possibly. But both forms of "to have" are nearly completely interchangeable and perfectly acceptable :)
I'm not a native speaker, and I usually listen to Western radio so I cannot say much about the language of Kyiv (other than it is the standard language). You can find some info on it here: http://www.encyclopediaofukraine.com/pages/S/T/StandardUkrainian.htm
The Kyivan dialect is the form we use on Duolingo. Not the L'vivan or Transcarpathian dialects (though those Hungarian loan words sound amazing!).
There is no such thing as Kyivan dialect.
Unfortunately I have no time to go through the Ukrainian Duolingo, but what I can see from the discussion that some items are ... disputable.
If you listen to news on Ukrainian TV channels, which are available on the web, you'd find that even central stations have different ideas about the Standard Ukrainian. The general trend is to remove the communist legacy which was intented to diminish the differences between Ukrainian and Russian, as also mentioned in the last paragraph in your reference.