Kotlin was created to solve developer challenges of JetBrains company. Soon, it became a popular language for Android development. However, the guys didn’t stop there and designed Kotlin/Native, the technology that allows writing native applications.
You have a wonderful set of questions. Unfortunately no one has a crystal ball to predict the future. However, from some basic observations and logical deductions, it can safely be said that Google is behind Kotlin and Apple behind Swift, so they are two distinct streams.
It is a possibility that Google might adopt Swift too, but it will be very difficult to imagine Apple adopting Kotlin officially.
For cross platform purposes, there needs to be something because there is too much language and tech fragmentation already. It is not surprising that Xamarin is finding itself popular in enterprises.