Hello
first, sorry for this very late answers:
parasitic capacitance approximated in eDesignSuite corresponds to the intrinsic capacitor caused by the spacing between spiral wires. It is a parameter of the antenna equivalent model that causes the antenna to have a self resonant frequency, that is a frequency were impedance changes from inductive to capacitive.
Additional tuning capacitance that could be necessary to reach the right tag tuning frequency when the antenna impedance is not right is not part of eDesignSuite calculation.
AC0 and AC1 pins are Differential RF inputs. For all our products , AC0 and AC1 shall be connected to the antenna coil, with no low impedance path to Vss pin (ground pin) if any.
Best regards,
Henry Crane NFC/RFID support team