Can someone please let me know what email address may I use with PHP list?

Can someone please let me know if I need a domain name and associated email address in order to use PHP list ?

In other words , does the PHP list gets connected to a third part mail server ?

You use the one that you have access to, be it part of your domain where your phpList is installed, or your gmail/hotmail one.
Just add the settings to your config.php file. (You’ll find the basic layout in the configextended.php file, copy this, fill in the details to match your email access and add to the config.php file)