We need 2 scripts in PHP:
One that performs Facebook Login using their api+sdk, and then, right after the sucessful login, it catches the 15 last user's posts ( feed ), and basic informations from each post, such as likes, comments, text ( message ), link, image ( if any ), video ( if any ), everything about each post. We dont need to read comments, or informations about who commented, or shared, we just need to total number of interactions.
In case the script finds an specific post, with an specific hashtag, the script must save this post informations into a MySql database for future use.
Another script that access that specific and saved post in order to check if it's still there, if its still public, check the numbers again ( share, likes, comments ), etc.
Let me know your thoughts.