Updates:
1. The Allegiance dailies don’t give a black key every single day as originally stated above. But very frequently.
2. It is not necessary to complete all the Lore pages in all zones in order to finish Allegiance rep. It just helps a lot on your first toon, to get those boxes full of points.
3. Weekly allegiance quests: reset on Monday, and you will lose the quest from the previous week, if it is still in progress. Once you take the new one, you have a set of objectives to wok on all week. Some of these will overlap with the dailies (same zones, same instance, etc). If the weekly is for instances, see Candur in Udun. Sometimes the weekly takes place on landscape (eg, roaming Scourges all over Mordor).
4. Rare Mordor chests: Popular wisdom (cited above) was wrong imho. The items inside the chests are rarely if ever first class cap items. Your toon will benefit more by opening them as you level through each zone, while you are below cap.
5. Meta deed: confirmed that it is needed to open dailies, along with reaching max rep with your allegiance.