Is it possible to create an Outlook PST file on my personal home computer and somehow link that to my Yahoo email account? My home computer is not part of any network but I'd like to be able to save emails on my computer's hard drive rather than leaving them in folders within my Yahoo email account.

It depends whether Yahoo mail will give you POP/SMTP addresses to sync with them. Most of the time you have to have a paid service in order to be given POP/SMTP authentication...

Edit// I looked up an article for you that describes how to do this.