1) Does Dark Necrofear's effect works on either player's End Phase?
Yes, it works during the End Phase of whatever turn it was destroyed.
2) What is a die roll?
What it is meaning is that you roll a die for the Archfiend monsters effects, most of the Archfiends have effects that say you can roll a die when a card targetting it is activated and if you roll specific numbers then it is negated and destroyed. That's what that is pertaining to.
Netrep Card Registry states:
[tt]6. If "Dark Necrofear" attempts to equip itself to an Archfiend monster and the Archfiend die roll is successful, "Dark Necrofear" will be destroyed and sent to the Graveyard.[/tt]
3) After Necrofear is destroyed while being treated as a equip spell card, is his effect still active?
Necrofear's effect can only activate once per turn. So if for instance activates in the End Phase and equips to Gearfried the Iron Knight, it would be destroyed by Gearfrieds effect and since it already activated that turn, it cannot activate and will not activate again, unless it's special summoned back onto the field from the graveyard and destroyed once again by battle or by an opponent's card effect. However if she is destroyed by an opponent's card effect while equipped to a monster at a later turn (destroyed by an opponent's Heavy Storm, MST, Dust Tornado, Harpies Feather Duster, etc.) then she will activate her effect again that End Phase and equip again. If the monster she's equipped to is destroyed, she will not activate because equip cards on monsters that are destroyed are simply sent to the graveyard, not destroyed.