The path is normally not needed. It would only be relevant in very special circumstances if the API has been mapped to a URL path. You should leave it empty.
The wallet passphrase should match whatever you have set as your walletpassphrase when you encrypted your wallet. You only need to set this if you want to enable withdrawals, and only if you have encrypted your wallet (you should).
To connect to a remote wallet, you first need to make sure that your firewalls are configured correctly on both ends. If they are not, you will get connection timeouts which will slow down your site.
You must also do ssh tunneling (see https://en.bitcoin.it/wiki/Enabling_SSL_on_original_client_daemon) to make sure that communication is secured. It has been requested of me to add instruction on how to do this but I have not had the time to attempt it myself. So I cannot provide instructions. This is a question better suited to the Bitcoin core wallet developers.