This never seems to be specified in the books. What's the consensus - is an invite past a threshold permanent? Once invited, always invited? Or does it only last until the invitee leaves?
I think it's for one stay only, though it's rather vague. The laws of hospitality work both ways though, so I would argue that once someone officially leaves in the spirit of hospitality, the invitation is void. By spirit of hospitality, I mean that the visit is over, they didn't just leave the house. So just stepping out once wouldn't end the invitation, but saying goodbye and leaving would.
In the books you occasionally see non-sponsored magic in the hands of laypeople who likely don't have spellcasting powers. Thomas uses multiple tracking spells, for example, in one short story. I also believe Harry teaches a couple of people how to make a magic warding circle. What's the consensus on how that is being done?
I could see this as being a 1 trick pony sort of thing. You could reduce ritual to a 1 refresh power, only allowing you to do 1 specific spell. It would be a character with very weak magical talent. I don't really know about Thomas though, haven't read that for a while. Didn't he work with Bob there? That could definitely be sponsored magic to a degree. Or maybe Thomas simply has some weak magical talent, due to his mother.
A lot of times, something like this might just be handled with a Fate point. Thomas could say "Because my Mother was a wizard, and I've seen my brother do this a lot of times, I should be able to get a half decent tracking spell running", pay a Fate point and be done. Or in the case of the coven, it might even just be something that happens in the background, without any actual power attached to it.
The rules do not suggest it can be done, but has anyone experimented with allowing someone with evocation/channeling to use magic in defense rolls? Rereading the books, it doesn't seem like Harry is using his "action" to activate his shield bracelets. Or is that a function of the focus item itself?
"I readied my shield bracelet" can easily be translated as "I create a block using magic" in game terms. Mechanically, the shield would come into existence right there, but in the story, it only appears one it is used to deflect an attack.
I will allow some enchanted items to be used reactively as well, blocks are among them. Though I usually use the rule that if you use the block item actively, it lasts for the whole duration it was intended to. On the other hand, if it is used reactively, that use will only count against this one attack, and it will not last for anything more than that. I think that's a good compromise.
In the vein of house rules, what's the thought on allowing focused practitioners to buy refinement in order to add bonuses to their specialties?
Well, specializations don't help them too much. Once they've got their +1/+2 filled, they can't get any higher, because the rules force them to keep at least a column build, much like skills.
I've proposed to go for specialized evocation, when it comes to channeling. The idea is to split the channeling element (or theme) into 3-5 subcategories and have them be your evocation elements. You can then buy specializations for those.
I think there's been the proposition of "blank specializations" somewhere, as well. That would mean that you can put points into blank specializations, which would then support your columns. You could have:
+3 fire control
+2 blank, fire power
+1 blank, blank
This would cost you 9 points of refinement, 4 of which would go into blank specializations.
I'm not sure how just removing the need for supporting columns would work out. The same column above could give you
+5 fire control
+4 fire power
+3
+2
+1
Since you'd have to allow this for wizards as well, I think, this could get lopsided pretty quickly.