The mic input is generally mono, with one channel providing the power supply to the mic (through a resistor). The capacitor is to block that DC.
Connecting the cassette head to the microphone input provides a simple way to read a magnetic card. The track data is self-clocking, and in the cards I read (a student card, and a bus pass) years ago gave results similar to those shown in
http://www.gae.ucm.es/~padilla/extrawork/soundtrack.html (there's also software available there for reading & decoding to binary).
There's an attachment for phones (Square) that does exactly what you're writing about (allows credit card details to be read and sent to an online store), with the recorded signal shown in
**broken link removed** and
**broken link removed** . You can see that the signal is being overdriven a fair bit, but is still readable.
Details of the data on track 2 of the card
http://en.wikipedia.org/wiki/ISO/IEC_7813
So in short, yes, it's possible and not complex. You'd be best to process the PCM data on the user's computer, and sent only the decoded data to your shop server (w/ SSL).