Credit Card Sized BT receiver, circuitry, eink display and power supply. Possible?
Something 2-3mm thick is pretty feasible. Various people have done similar things as "electronic business cards" or "programmable badges".

E-ink is a bit of a pain as it requires suprisingly high voltages compared to 1.8V logic. Normally done with a boost converter, but that's another thing you have to flatten. A regular LCD would be easier.

The self-rewriting magstrip is a serious problem; you might be able to emulate it with a magnetic loop that varies at the right rate.