Can we perform Perumal Tiruvaradhanam after performing tharpanam on the banks of Kaveri? Is there a rule that pitru tharpanam is to be performed only after Perumal Tiruvaradhanam?

It is better to perform pitru tharpanam after Perumal Tiruvaradhanam; having said this, in a few traditions, Perumal Tiruvaradhanam is performed after doing pitru tharpanam on the banks of Kaveri.