Diablo – Does Nagelring Proc with Zunimasa 6 set bonus

If an items does 10 - 15 base-damage and you put in a gem that adds +2 min / +2 max the new damage range is 12 - 17 damage.

Before the patch, the calculation was exactly the same, but +2-4 damage is much more confusing (in my opinion). The new wording just clarifies what really happens.

EDIT:
Explanation of the old tool-tip: the damage modifiers of rubies (and +X min or +X max) on a weapon are calculated before other damage modifiers (like elemental damage for example). Within this, the +X min get applied first, taking our example weapon from above to 12 - 15 damage after this, the +X max gets added, resulting in said 12 - 17 damage.

If we get another weapon with a very small damage range like 10 - 11 damage it works the same - but after the +X min is applied, we get 12 - 11 damage which doesn't make sense. As a result, the max-damage is raised to 13 and then the +X max gets added, resulting in 12 - 15 damage. We ended up with +2 min / +4 max.

Now, if we take a weapon with 10 - 10 damage (no range), we theoretically end up with 12 - 15 damage again, which is +2 min / +5 max (or +2-5 damage) but this doesn't happen in game as there's always a damage-range, so this possibility was excluded from display.

Conclusion: the old tool-tip showed the theoretical maximum effect a ruby could have, which doesn't really happen in-game. Even my second example only happens rarely (only if you put a high ruby in a low-level weapon) so the new tool-tip is much more exact.

Unless the bonus is identified on the items, no. In your example, putting on four pieces of Cain's Fate would not give you an additional bonus over putting on three pieces.

If, for example, you picked up a set that had bonuses for 4 or 5 pieces, then these sets would give additional bonuses as detailed on the items for equipping more pieces of the set.