Exception thrown inside catch block - will it be caught again?

No, since the new throw is not in the try block directly.

No. It's very easy to check.

public class Catch {
    public static void main(String[] args) {
        try {
            throw new java.io.IOException();
        } catch (java.io.IOException exc) {
            System.err.println("In catch IOException: "+exc.getClass());
            throw new RuntimeException();
        } catch (Exception exc) {
            System.err.println("In catch Exception: "+exc.getClass());
        } finally {
            System.err.println("In finally");
        }
    }
}

Should print:

In catch IOException: class java.io.IOException
In finally
Exception in thread "main" java.lang.RuntimeException
        at Catch.main(Catch.java:8)

Technically that could have been a compiler bug, implementation dependent, unspecified behaviour, or something. However, the JLS is pretty well nailed down and the compilers are good enough for this sort of simple thing (generics corner case may be a different matter).

Also note, if you swap around the two catch blocks, it wont compile. The second catch would be completely unreachable.

Note the finally block always runs even if a catch block is executed (other than silly cases, such as infinite loops, attaching through the tools interface and killing the thread, rewriting bytecode, etc.).

The Java Language Specification says in section 14.19.1:

If execution of the try block completes abruptly because of a throw of a value V, then there is a choice:

• If the run-time type of V is assignable to the Parameter of any catch clause of the try statement, then the first (leftmost) such catch clause is selected. The value V is assigned to the parameter of the selected catch clause, and the Block of that catch clause is executed. If that block completes normally, then the try statement completes normally; if that block completes abruptly for any reason, then the try statement completes abruptly for the same reason.

Reference: http://java.sun.com/docs/books/jls/second_edition/html/statements.doc.html#24134

In other words, the first enclosing catch that can handle the exception does, and if an exception is thrown out of that catch, that's not in the scope of any other catch for the original try, so they will not try to handle it.

One related and confusing thing to know is that in a try-[catch]-finally structure, a finally block may throw an exception and if so, any exception thrown by the try or catch block is lost. That can be confusing the first time you see it.