I’m going to install Android Studio 3 in order to develop an Android application.
I’d like to know if it is possible to use Java 9 for Android development? If so, does it support all of the Java 9 features?
As far as I know, the IDE itself supports Java 9. This means you can write a Java 9 desktop program, or run the IDE with JDK 9.
However, Android itself does not support Java 9 (yet). You can still download JDK 9, although I have seen some questions on problems related to Android Studio and Java 9. Personally, I have Java 9 and Android Studio runs without problems.
The Android SDK is the development kit you’ll be dealing with, and with source compatibility you’ll get language features similar to Java 6, 7, or 8, depending on your settings. So you can download JDK 9 and use that most likely without issues, but you can’t use any of the language features in any Android apps.
As for differences between the JDK and the Android SDK, you should read this. Android currently supports a subset of Java 8 features, but not everything. It might never support everything, or leave out some parts of Java 8, even if it later supports some parts on Java 9 or higher.