A modern programming language that makes developers happier.

kotlinlang

In *Project Structure* for my Kotlin project, in the section *Project Settings\Project*, what is recommanded for these settings:
1) *Project SDK*: Should it be the java version  that fits with my JAVA_HOME variable? Should it be *Kotlin SDK*?
2) *Project language level*: Should it be set to *SDK Default*? Should it be set to an explicit level?

Project SDK should point to a Java JDK. JAVA_HOME is typically just a JRE.
Project language level depends on your use case. Do you want to use features from the newest java versions? Use a new java JDK and set it to SDK Default. If you want to restrict your project to features from JDK 8, set it to level 8.

This is the case for all my Java and Kotlin-JVM projects. I do not recall being able to use "Kotlin SDK" and it working. My answer is from personal experience.