Yes. Actors are labor, not management, so their understanding of what's going on at the executive level is second or third-hand.
They can do either. They own the characters, after all -- or rather, DC owns the characters and Warner Bros. owns DC. It's not hard to understand that if someone owns something, you need to ask their permission before you borrow it, and they're entitled to say no.
Yes, that's just the point -- "embargo" is the wrong word. It implies a blanket prohibition that Warner Bros./DC has handed down, when actually it's a case-by-case determination. It's the difference between "No, I will never let you borrow my car under any circumstances" and "I'll consider letting you borrow my car if you ask me, but I might say no depending on the circumstances."
For instance, it used to be the case that there was an embargo on using Wonder Woman in any screen production where she was a guest character instead of a lead character. It was meant to protect her prominence as a character, but it backfired, because it rendered her largely invisible. It's why she never showed up in the DC Animated Universe until Justice League, where she was a member of the core ensemble and thus a lead character, and why she was the only JL core member who never guest-starred on Static Shock. Under an embargo, there were no exceptions to the ban, so she appeared less than she could have. Once the embargo was lifted, then it was decided on a case-by-case basis, so she could appear as a guest star in the final season of Batman: The Brave and the Bold.
