I have a Facebook "fan page" for my acting career (I mean a page that I created within my personal FB account) I want to make the feed from this page appear on my personal website as a "news feed" for publicity reasons. My website developer tool has a "custom HTML" option that has allowed me to make my Twitter feed appear on the webpage, but I want to use my Facebook page instead.
What you are searching for is the Like Box which has option to display your Page's stream on your website. Features about the like box (Quoting from documentation)