Is there any way to add cards to my wallet WITHOUT a 3rd party app like it tries to give me when I tap the + button? With WP 8 you could select the kind of card (visa, other...). Is this possible with 8.1?
Yes, you can add additional cards by downloading the .mswallet file from the provider's website. There is a quickstart guide that you could point your local, friendly, library at, if they don't do this already (or you could roll your own, based on that documentation)