Here are some things about the endgame Minas Morgul rep and dailies:
When you finish the Minas Morgul quest lines, you will find daily quests to go with the instances. There are now 4 instances for groups of 1, 2, or 3, 2 instances for groups of 1, 2 or 6, and one only 6. Higher tiers are available for 3s or 6s.
You can run the instances (if you have discovered them) at 121-130. The first 4 were required for the quest lines.
The gear/rep grind is from the quests that go along with them. There are also other quests and weeklies.
The quests reward Relics of Minas Ithil (200 rep), Well-preserved Relics of Minas Ithil (1,000 rep), or Pristine Relics of Minas Ithil (2,000 rep).
If clicking on them to raise your reputation, always use a reputation tome.
The relics can also be bartered for gear as well as recipes for gear. The gear is organized in tiers based on your rep. You probably want to wait until you reach max tier before you invest in recipes or gear. The gear is available at lower tiers, but it is common, so may not be better than quest gear.
The rep items are account bound, so one character can pass them to another.