Rep 5 and 7, iirc. You need to have a hideout large enough for the masters you want to invite.
More rep = larger hideout. You can swap hideouts willy-nilly, nothing gets lost.
I would suggest the Path of Exile wiki for more in-depth info. Because honestly, I maxed out the masters ages ago and don't remember the details.
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They are not consumable. You can reclaim the effect.
What you can do is sell and drop the item with the effect and lose that effect. So, pay attention.