Yes, it is - I develop Cursive and I don't work for JetBrains.

That said, even though Cursive is third party, the way that IntelliJ is designed means that language extensions all tend to work in consistent ways. Rather than totally reinventing the wheel, I basically plug into standard IDE workflows for different types of extensions, and make them work for Clojure. This means that Cursive is able to feel like a JetBrains product, although sometimes less polished because I work on it on my own.

It's one of the things I love most about IntelliJ, all the support for different languages basically works in the same way and it's very easy for me to pick up a new language if there's support for it.

Can I create plugins or modify intellij itself using clojure?

You can, and Cursive is partially written in Clojure. I don't recommend it though, I'd definitely recommend using Kotlin.