Is there any programming contests and/or problems site that currently supports Kotlin?
I could not find any except for try.kotlinlang.org, old Kotlin Challenge at Codeforces (which I unfortunately missed) and my university homework server (which had an outdated version that time).
Are there plans of promoting Kotlin usage in contests?
As far as I know the most polyglot contest platform is www.hackerrank.com. You can see the list of supported languages here. May be they could adopt Kotlin
Thanks, I wrote an email to hackers@hackerrank.com asking about plans to add Kotlin support. Let’s wait and see. 
http://adventofcode.com/ doesn’t have any restriction regarding the programming language and using Kotlin was really fun.
Here’s what HackerRank support said:
I really appreciate you taking the time to bring this to our attention. I’ve passed this to our engineering team who can check this and make improvements where possible.
Yippee, Codeforces added Kotlin to supported languages!
I made a request to https://www.codingame.com/
I’m too. ) But they plan to support Kotlin first on tech.io.
Kotlin support has recently appeared at Hackerrank too.
And, most notable, Kotlin became official language for ACM ICPC programming contests:
but still not for all the tasks =(
I really wonder why all platforms only support Kotlin/JVM but not Kotlin/Native?
I usually have Time Limit Exceeded error on spoj.com with Kotlin/JVM even with the optimal solution.
Sometimes I tried to do some tricks to improve runtime performance and passed, but it shouldn’t be the way to go.