I confirm Example 1.
Jace's Mindseeker has the same exact wording of
Summons of Saruman (
"You may cast an instant or sorcery spell from among them without paying its mana cost.") and has the following ruling:
If the five cards are put into a public zone such as exile instead of a graveyard (perhaps due to the ability of Rest in Peace), you can cast one of those instant or sorcery cards from that zone. (2013-07-01)
The
library is
not a public zone (I've used
hidden, which may not be the correct terminology, but the point still stands), so you can't cast
Nexus of Fate.
Conversely, if the Example 2 involved
Summons of Saruman, I'd say you can 100%. Since the wording of
Fallaji Archaeologist is slightly different, I don't know for sure.