I need my site to occasionally read a file in order to update itself. (Daily or weekly if possible)
Is php capable of this alone? (From what I’ve seen the answer is “no”)
What else can I use to do this? (Sql seems like it might work, but I’ve searched and can’t tell for sure)
You could use a cronjob that executes your php-script at a given interval (eg every day at 12pm).
In case you cannot use real cronjobs: there are also some sites that offer free “cronjobs” – you give them a URL and they visit it at the time you tell them to. Just google for “free cronjobs”.