Quests of Iceshard Keep must be finished if you want to zone the group in, but you don't need to finish the quests to enter the zone.
It seems 90+ is no longer a requirement to enter the zone, however most zone quests will not be available so characters below that level will not be able to progress in the quest timeline.
Begin clearing the zone but when you enter the first big room (Throne Room) and oversee the meeting, just stay there at a distance and listen in (you will see a message about a good spot from where to listen and it will update the quests) but don't get close to the non-aggro mobs. If you engage the mobs, you'll get to fight one right now and all the rooms will have their name mobs. If you have a good group and want to clear the zone faster, you can go this route so you don't have to backtrack to the clear rooms for their name mobs.
Go around and clear all of the rooms of trash mobs, including the throne room (it's best to start with Royal Kennel which is the first room to your right when you enter the Throne Room since it contains the key mob and one of the other rooms you will be clearing has a shard chest). Wolfmaster Oor will be the only available named inside Royal Kennel room, go ahead and kill him. He will have two named wolves Ragefrost and Treachery helping him. You can kill the keymob while in Royal Kennel.
Once all the rooms are cleared go approach the meeting in the Throne Room and Allectus Prime Karsgard will soon attack. Killing him will progress the zone and spawn remaining named mobs in all other rooms except for Royal Kennel. Go kill Decanus Prime Vundr in Grand Hall, Arch-Depracator Vorkin in War Room and Weapons Master Korin on Armory of Storms. The order of these kills doesn't matter and when you are done, it will spawn the zone boss, Tribunus-Prime Hagandr.
If you're doing the quest End of Immortality you will loot An Enormous Metal Key which can unlock an orc named Wolfsnack inside Royal Kennel room (there's only one key but whoever takes it will update the quest for everyone else in the group). The orc will continue the quest and take you to the throne and help you complete the sequence of lowering it in order to enter the Keep of the Horn. In that room you can dispel the horn to complete the quest. Once the horn is dispelled, the exit will be blocked by an Aureate protector (17M HP). Don't be fooled as this guy has a lot of HP and hits hard and he does drop a treasure chest despite not being a named mob (he has a very powerful heat attack called Fleece that hits for several hundred thousand hit points, it may be a directional attack).
You're done now, feel free to scour the zone for any missed shinies and exit out to claim your quest rewards.