1) They don't share fatigue. They're independent so if you hit the "chat" option for housekeeper A, they will get 15 fatigue. The others will not.
2) Yes, I guess so. I have one physical attack buffs and 5 others all for crafting so I can guarantee myself plenty of unbridled and galloping gales.
3) Yes, if I am understanding you correctly, yes you can have more than one embrace. My attack housekeeper for example gives 6% PATT and 1,200 attack power OR it gives physical critical hit rate but you can't have all THREE.
Adding onto what Acet said, personally I have two full physical attack NPCs, you don't necessarily get the buff (on occassion I've had really bad luck and not gotten it from all 8 uses from both my housekeepers).
That and if you do get your buff for siege or whatever it is you need it for you may end up running an instance later in the day or something so it's helpful to have multiple buff housekeepers.
As far as crafting goes, max all of your housekeepers with crafting, it's good if you don't get what you want from crafting most of the potions that are useful come from crafting levels below 80.
@3, Acet they're asking about having Protection and Magic, yes and no you can have them at the same time but it's overly complicated to and they get overwritten easily, you can have Mcrit and %HP or %Defense.
You can't however have it the opposite way unless you have low level protection buffs since the protection npcs always give a % buff.