Magread is an already proven app that uses a free audio port magnetic card reader from Square to accept credit cards. While Square may have an unusable encrypted interface with Magread we can already quickly read the required credit and debit magnet strip cards even if there is not yet any server side connection to a payment service able to use the card swipe.
Is there a e-commerce solution that has an open API to quickly swipe in the card data, have a customer punch a PIN, and enter a price total for us to have an open-square type money transfer using HTTPS rather than whatever Square uses and pocket size point of sale services. It seems that some bank or perhaps paypal already allows such transactions. I can imagine anything from selling trinkets on a blanket, to roadside bike repairs, to home delivery of baked goods benefiting from an easy working non-square monopoly credit/debit card acceptance app for maemo and other OS's.

Does anyone know if there any bank APIs that could use either the Square reader for transfers/deposits or if they will accept photographed checks for deposit?

No, their API isn't open yet.