Sernario 1: Player A casts portent on Player B and insturcts them to shuffle. Does player B have permission to view the top of their deck (which Player A viewed before having them shuffle).

Sernario 2: Player A finishing resolving Brainstorm and passed priority. Player B casts a surgical extraction on something in Player A’s graveyard which resolves. Does player B have a right to know what the top 2 cards put back by brainstorm are?

With senario 1, I can find nothing giving Player B permission to view their deck while shuffling. Note that the common crack a fetch, check the top card after a Jace plus is different as a fetch causes a search.

For senario 2, I believe Player B is entitled to that information, as deck order must be maintained during a search.

Thank you

Scenario 1: if Player B looks before shuffling, it would (at Comp REL) be Looking At Extra Cards. Players can't look at cards in hidden zones, unless an effect tells them to.

Scenario 2: Player B will see the entire library while resolving Surgical Extraction. I'm hesitant to say it's a “right”, as that's not really a concept defined by the rules. If you prefer to think of it as their right, no harm done.

Note that, if A were to shuffle their library and then hand it to B for the Surgical search, it would (again, at Comp REL) be a Game Rule Violation; players can only shuffle a library when a game mechanic (e.g., pre-game procedure) or a card's effect tells them to.

d:^D