If I cancel my now published PCT, I understand it will be prior art since it is revealed to the public domain. However, what will be the date that this cancelled published PCT will be considered as prior art? Is it going to be its original filing date or its publication date? I am looking to claim priority over a separate application I filed before the publication of my PCT and after the filing of my PCT. I wonder if this will be possible by cancelling my published PCT.
The publication date. Documents become prior art the day they are disclosed to the public, which in the case of international applications (PCT) and patent applications is whenever they become public.
The way I understand your second question is that you filed another application (P1), and you want to claim priority from it in yet another application (P2). You can do so as long as you file P2 within the 12-month period starting from the filing date of P1. You can only benefit from the priority of P1 for that matter for which P1 is the first application. So if your PCT disclosed some matter present in P1, then P2 will not validly claim priority from P1 for that matter.
P.S. 'Cancelling' a PCT that is already published does not help you in any way. Let it become abandoned. Perhaps you will change your mind by the 30/31-month period and you will want to enter into some phases, by actively abandoning it you lose that right.