a.) I thought I had the Java 8 JDK on my Mac? Or did I just have the Java 8 JRE?
Well, would seem like you at least don't have all the Java components Libre Office expected.
b.) How can I tell?
The Terminal command mentioned earlier on.
java --version /java -version
depending on specific variant of Java.
It shows the version of the Java runtime and server.
Then "javac -version"/"javac --version"
shows the version of the Java compiler
Pretty darn sure you won't have the compiler if you don't have the JDK.
c.) Can I downloaded the Java JDK for free?
I downloaded it for free at least.
Here's from Oracle's website:
"
- End users and developers looking for free JDK versions: Oracle OpenJDK offers the same features and performance as Oracle JDK under the GPL license.
"
It is also what homebrew installs.
d.) Am I going to have to register with Oracle?
Shouldn't be necessary
e.) Do I install the JDK over what I have, or do I have to uninstall Java 8?
No need to uninstall anything. Hell, you can even have more than one Java version at once if you want - like different version numbers. I have 6, 8 and 12 on my iMac.
f.) Am I going to break other software using Java by doing all of this?
Nope. If any of your other software needs a specific version, you can keep that version too, but there should be no compatability issues anyway.