I'm afraid I don't have the time to watch the entire video but, being a physicist, I can still try to answer your questions. Currently, however, your question
> If time becomes space-like, and space becomes time-like, can we think of black holes as "time stars"?
doesn't make much sense to me. Time does not become spacelike nor does space become timelike. In General Relativity, time and space are not individually defined in an observer-independent fashion in the first place. The terms we use instead are "timelike directions" and "spacelike directions" as well as timelike / spacelike hypersurfaces because they are defined in such a way that all observers will agree on whether a direction / hypersurface is timelike / spacelike. So now that we've replaced the terms "time" and "space" with "timelike" and "spacelike", I hope you'll see that your question is not exactly well-defined.
But maybe I'm misunderstanding you, so please feel free to elaborate on your questions. (Or to point me to an explanation from the video in case you're referring to one.)
As for your second question:
> Would every black hole within our observable universe contain information from all light cones within the observable universe? In other words, would different black holes contain different information?
I'm afraid I can't follow this question, either. Would you mind rephrasing it? My initial impression is that you might have a wrong idea of what a lightclone is.
I just realized I was replying to the wrong parent comment! So sorry. I was talking about a PBS Space Time episode on YouTube I saw in (or came across via) a different comment.
Judging from the few minutes I watched, it is at least not very precise, yes.
What they mean when saying that "time and space switch roles inside a black hole" is that in standard
Schwarzschild coordinates, the direction given by the time coordinate becomes spacelike at the event horizon and, likewise, the radial coordinate becomes timelike. This statement is specific to Schwarzschild coordinates, though, or, more generally, any coordinate system that is singular/ill-defined at the event horizon. There are coordinate systems, however, that don't exhibit this pathological behavior at the horizon and, there, no switching occurs.
> If time becomes space-like, and space becomes time-like, can we think of black holes as "time stars"?
doesn't make much sense to me. Time does not become spacelike nor does space become timelike. In General Relativity, time and space are not individually defined in an observer-independent fashion in the first place. The terms we use instead are "timelike directions" and "spacelike directions" as well as timelike / spacelike hypersurfaces because they are defined in such a way that all observers will agree on whether a direction / hypersurface is timelike / spacelike. So now that we've replaced the terms "time" and "space" with "timelike" and "spacelike", I hope you'll see that your question is not exactly well-defined.
But maybe I'm misunderstanding you, so please feel free to elaborate on your questions. (Or to point me to an explanation from the video in case you're referring to one.)
As for your second question:
> Would every black hole within our observable universe contain information from all light cones within the observable universe? In other words, would different black holes contain different information?
I'm afraid I can't follow this question, either. Would you mind rephrasing it? My initial impression is that you might have a wrong idea of what a lightclone is.