In Java Security exceptions there must be both
If you want to use the default client you'll need to have enabled Java for your Browser in JCP (but leave it disabled in Browser settings) otherwise you won't get a prompt to choose the Java Web Start Launcher for jnlp files. (manually you can open autohaven with javaws in Java\jreX\bin)
The default client (Play Button) doesn't need a run.bat - that is for starting custom clients on Windows, on LInux it's run.sh and on MacOSX it would be run.command - more here:
viewtopic.php?f=27&t=31594#p490847which would also be the right thread to post if there are more questions about running HnH custom clients on OSX
I also recommend to check if you have the latest updates for your OSX version -> Graphic drivers
(If you bought your MAC in a local store just create a folder called Ender, download the updater.jar into it, run it by doubleclicking - then go to your local store and let them help you with creating a run.command inside Ender folder and help you to run it - with the prices Apple takes there should be some support possible

)
hth