I know that in the API users must allow the app permissions to use their specific user data. 
But as a user, I have friends which have their own likes. Is there a possible way to query another user or my friend's profile (using their user id) to get a list of their likes via the Graph API. 
Ie. because they've decided to friend me, they've given me their permission on a user basis to access their data in Facebook, so can I query this via the graph api as myself instead of an external app?
No, that is not possible.
What is visible/accessible to you as a user on facebook.com or in their official apps, has litte correlation to what you can see via API.
If you want to access anyone’s likes via API – then they have to login to your app first, and grant it appropriate permission.
How to use Facebook graph api as myself instead of external app, to query friend's data?