You'd think you would get a bedroom in the keeps since, you know, you run the inquisition? I guess they just kick out whatever random dignitary is there for the night and make him sleep on the floor to give me a bed...at least I like to think so. 
Each of the keeps are main parts of the zone storyline (Western Approach actually is an "offshoot" which you don't have to take, while the Crestwood and EDL keeps are central to the story line. Crestwood so much so that you cannot complete the main quest in the zone without it), but none of them are required to complete the game / main quest line.
That said, several inquisition perks require you to capture at least 1 keep to be able to get the perk, which is important. Also, the crafting crap obtainable from the missions the keep unlocks is top notch...for instance, the keep in Western Approach is providing me Everite (Tier 3 Metal) at a rate of ~6 / 15 Minutes...unreal. In about 10 - 12 hours of play, I'm sitting on 90+ Everite...which is working really well when I go to craft something. 
Resource Gathering Operations unlock the moment you've unlocked a zone...so you can gather resources from EDL the moment you unlock EDL, leave the war table, and return...you'll see a War Table Mission at that point allowing you to gather resources.
Liliana provides Only Herbs, but in large quantities.(3-6)
Cullen provides Only Metal, but in large quantities (3-6)
Josephine provides both Metal and Herbs but in half quantities.
Regardless of what the text description says (like EDL's notes Silverite and Felandarus) you do not get different materials from the mission.
Hinterlands: Elfroot, Onyx and Drakestone
Fallow Mire: Blood Lotus, Dawn Lotus, Summer Stone, and Blue Vitriol
Crestwood: Embrium and Obsidian
Western Approach - Deep Mushrooms, Paragon's Luster
Emerald Graves: Embrium, Pyrophite
Exalted Plains: Rashvine and Veridium
Emprise Du Lion: Arbor's Blessing and Bloodstone
Hissing Wastes: Deathroot, Lazurite
Taking a castle in a zone opens an additional mission to gather specific resources. Black market is the most valuable, and despite the description, you don't seem to have the possibility of returning nothing. That said, Leliana is the only one that can go to the Black Market, so as with the rest of the war table, she seems to be your choke point. Cullen returns junk, Josephine returns half of what Leliana returns and half of what Cullen returns.