As for the time hijinks with the creation of Bec Noir, I believe that Vriska had a choice there as well. If she hadn't been willing to create an unkillable endboss for herself to kill, the timeline where she did would never have come to pass.
This is all speculation on my part, but I really don't see how else it could go. There has been no instance in the story of a character learning of a future that he is forced to play out but doesn't want to. Dave's time loop shenanigans are completely in character, as are Karkat's endless arguments with himself. The players aren't forced to play out a predestined future, but the other way around. The future is what the players choose to make it, upon hearing about a future. Timelines that the players would be unwilling to bring about do not exist.
For example, consider a timeline where John, quite out of nowhere, decides to
murder Jade. If John was to learn of it, would he go along with it, just to fulfill the time loop? If Jade was suddenly murdered by a time-traveling John, let's call him John-2, would John-1 feel compelled to travel back in time to murder Jade to complete the loop? If he didn't, what would happen? If he did, could he claim innocence, saying that he was forced to do it by predestination? Would John still be a likable character if he did it?
There hasn't been a single situation like this in the story, and I see no reason to assume that there even could be within the time travel mechanics provided. There is simply no situation where John would murder Jade for no reason, thus it does not happen. He has free will. To avoid a bad future, you simply need to be
unwilling to play along, and the bad future will never exist to affect the past!
Thus, Vriska is fully responsible for creating Bec Noir. She didn't actually actively decide to, at any point in time, but she was
willing to create him upon seeing that he had been created. Had Vriska refused to do it, Bec Noir would never have existed, and she would never have been given the choice she made in the other timelline.
Also of note is that both time players we have seen are very willing to follow a predestined path. Aradia as a robot ghost frog was slightly annoyed at having to take orders from herself to simultaneously orchestrate and bring about the final timeline, but she was still willing to do it. Dave had no problem whatsoever taking orders from Terezi to manage his stable time loops. When confronted by his sleeping time copy during the god tier gambit, he asked her what he was going to do, not wanting to actually make the choice himself.