There is an API call to find the subscription details etc, but what if I want to check all the subscriptions that a user has purchased? There's no API for that?
There is not. One of your users could have activated subscriptions with different payer accounts -- or a payer account could have been used to activate multiple users. It's not a 1:1 relationship (unless you were to enforce it) so you need to track this information in your own database.