Does a finally block run even if you throw a new Exception?

Yes, the finally blocks always runs... except when:

• The thread running the try-catch-finally block is killed or interrupted
• You use System.exit(0);
• The underlying VM is destroyed in some other way
• The underlying hardware is unusable in some way

Additionally, if a method in your finally block throws an uncaught exception, then nothing after that will be executed (i.e. the exception will be thrown as it would in any other code). A very common case where this happens is java.sql.Connection.close().

As an aside, I am guessing that the code sample you have used is merely an example, but be careful of putting actual logic inside a finally block. The finally block is intended for resource clean-up (closing DB connections, releasing file handles etc), not for must-run logic. If it must-run do it before the try-catch block, away from something that could throw an exception, as your intention is almost certainly functionally the same.

Yes.

See the documentation:

The finally block always executes when the try block exits.

Exceptions:

Note: If the JVM exits while the try or catch code is being executed, then the finally block may not execute. Likewise, if the thread executing the try or catch code is interrupted or killed, the finally block may not execute even though the application as a whole continues.