But "officially" no. And PFS is a no too
I believe the Unchained text states that you have to pick one or the other, but that an original rogue and an unchained rogue can exist in the same group together subject to GM discretion.
No, they cannot. You have to choose one or the other.
However, I think most GMs will allow rogues to choose either or.
When it comes to barbarians, as a GM I would make you choose either Unchained or normal, and the other is not available to you.
Many of the rage powers the normal barbarian gets are much stronger the "equivalent" powers that the unchained barbarian gets. And then there are a few (stance rage powers) that would be worth it to a core.
There's just too much overlap and too many things changed, I think it's easier to just keep them separate.
But what about the Viking Fighter archetype who can select Rage Powers?
Again, Viking fighter would be limited to only normal barbarian rage powers and rage functionality.
Unless the GM wanted to allow it otherwise.
Again, I would not be inclined to do so.
From what I remember from the entry in the unchained barbarian section, there is a restriction on it preventing it from taking older rage powers but there was no restriction placed on the old barbarian or any other rage power gaining class preventing them from selecting the unchained powers.
Again, Viking fighter would be limited to only normal barbarian rage powers and rage functionality.
Unless the GM wanted to allow it otherwise.
Again, I would not be inclined to do so.
Where can that restriction be found?
I believe Mark Seifter talked about it in a post he made.
That specifically Unchained Rage and Rage Powers were meant for the Unchained Barbarian only (only it was more general to say the the abilities of Unchained classes were designed only for them). Someone had specifically asked about clerics with access to the rage subdomain IIRC.
However, it is within a GM's power to extend it to anyone.