For iOS, it would be reasonable to think of Kotlin->Java as swift->objc. but not for server side. Kotlin is merely an alternative for Server Side on JVM as there's also Groovy, Scala, Clojure,...
And IntelliJ IDEA is the IDE of choice. Eclipse can be used as there's a Kotlin plugin for it too, but most would agree that IntelliJ is the more powerful of the two.