Quantum Predictive Model Questions
The important rule here is that when multiple triggers happen off the same event the active player's triggers happen first. And a player gets to choose the order in which effects they control happen.
With that in mind...
The first question depends on whose turn it is when the runner accesses QPM.
During runner's turn the runner would be able to place QPM on Film Critic. Since both cards have the same trigger - &quot;when accessed&quot; - the person who's turn it is goes first, so Film Critic would take priority.
However, if the runner somehow accessed QPM while tagged on the corps turn (such as with An Offer You Can't Refuse) then the corp would score it, because on the corps turn QPM would take priority.
The second question the corp gets to choose who gets the agenda.
Since both Casting Call and QPM have the same trigger of &quot;when accessed&quot; and both are controlled by the corp, the corp player chooses the order of resolution. Most corps would pick Casting Call to resolve first, giving the runner tags and then resolving QPM to give themselves the point. However, there are a few situations where the corp might want to let the runner steal it, (such as landing Midseasons) in which case they let QPM resolve first and give the runner the point.
The runner would steal QPM as they are not tagged at the time of access.
Per the FAQ :

Question: If a Runner with no tags accesses a Quantum Predictive Model that hosts Casting Call, does the Corp score the Quantum Predictive Model?
Answer: No. The Quantum Predictive Model does not resolve if the Runner is not tagged when the access occurs.