Personally, I'm fine with keeping the common lab, as originally proposed, with the hot mess of bonuses. It violates some rules, sure, but it's not doing it in a way to get +5 in multiple specialties, it's spreading all the bonuses all over the place, indicative of it being designed by committee. Imagine 4-6 magi doing this over time, and I can see the end result being the lab as proposed. I'd probably nudge the safety score a bit lower (maybe even hard rule it a 0), because the place is probably not in tune with Hermetic principles. Or swap the safety and warping scores around.
Yep. Magic. All ten of them.
Exactly. To the naked eye, they look like wood. Until you try to punch it in a fit of anger.
Especially since they've been tinkering with the thing for sixty or seventy years.
But I'll leave it to troupe discretion as to what, if anything, to do with it.
I think the process of petrification may have been understood, at least by the Venetians, as they sunk pilings of wood into water and mode and it turned into stone. Very possible that this knowledge is localized and kept quiet, like anything the Venetians of the period did. Still within paradigm, though!
However, we need more than 4 labs. We need 7, or at least any proposal should have enough to house every magus of the covenant. 4 would cover the PCs, but the NPC members of the covenant would be a might bit peeved if all the new folk came around tore down their lab and built 4 nice and shiny custom new labs (and sancta) in place of the common lab.
Especially the one with Inventive Genius and a double-digit Magic Theory.
But Doineann very rarely uses the Common Lab, due to her Restriction, so she wouldn't be that put out except on general principle. So we could get by with six labs.
Her restriction being surrounded by water?
It is simple enough to ask who wants to put a sanctum on Eilean Chon. I assumed the three existing magi would not want to move sancta, since that's a pretty big deal. Also, my proposal left the common lab intact.
The General Quality of +4 and the Aura increase to 6 give at least a +7 increase to any activity undertaken in the lab.
I'm not seeing how it might be reasonably preserved, if it's essentially centered to the island, you can't really build around it efficiently, and packing up and relocating the lab is problematic. "Let us preserve what must be preserved, perfect what can be perfected and prune practices that ought to be prohibited."
Can't cast spells indoors. Technically, that doesn't prevent her from inventing spells or enchanting items inside (as far as I can tell), but it does put a damper on things. That's why her lab is outdoors.
Would it be possible to build a temporary structure, with the same dimensions as the lab, cast The Ambulatory Laboratory to move the lab there long enough to get the new structure erected, and then move the lab back into the new larger structure the same way? It would still require, I think, that one of the labs be the same size as the Common Lab is, but it should preserve all the bonuses and stuff that the Elders have worked so long to build up.
I always thought Restrictions applied to all magical activity, but it might just be up to interpretation.
(If you have a Restriction against harming a human being, I would expect that you can't make a wand that casts Wound that Weeps.)
From an OOC standpoint, our characters may be in the process of designing the new structure on Eilean Chon when we discover a regio which is more appropriate for the new sancta.
Unless PB is going to houserule to allow transportation magics across regio boundaries, Halie can't put her existing lab in a regio (it's in Rome, and will be getting moved in with Ambulatory Laboratory in exchange for a small piece of her soul). So we could end up arranging for a second story on the existing cottage on Eilean Chon for Halie's lab (it is the same size), and put all the other sancta (and a dock for the Whoa Buoy) inside the regio.
Halie has +3 Perception and 2 in Second Sight, so she'll probably notice the regio entrance at some point. I like the idea of its entrance being on the water-- learn to swim, scrubs. 
"You cannot cast spells at all under certain uncommon conditions." (Although, I'm not sure "being indoors" really counts as "uncommon." Whoops...my bad 
) Further, it says "The Restriction also applies to effects generated by any enchanted items you create."
So, she can't cast spells indoors, nor would any magical items she makes work indoors. She could still extract vis from the aura, invent spells (that she can't cast atm), read and write whatever indoors, though.
IMO, yes. However, in this instance, the Finesse ease factor is a killer for the Per+Finesse roll of: 9+3*Refinement-3 (Disorganized)=18.
Out of the PCs Talia has the best: Per +Finesse of 7. So she needs to roll an 11 to pull it off, or the lab gains some flaws, twice.
If I do, it would also mean that not only could you apparate across regio boundaries, but that you could also cast other magic across the boundaries, such as Intellego...and Perdo. And so could everyone else.
Ya know what? Just for kicks, go ahead and give me a second sight roll.
This is why I made Ra'am's restriction barefoot on solid ground, like outside. He can't cast spells on Shabbat, anyway, so he doesn't really care those days. And then how many times would he go out barefoot otherwise? Yeah, it minimized the flaw a lot, but it does say, as you noted, uncommon. Of course steal his shoes and lure him outside...
Yes. Yes you could. Muhahaha!
OTOH if magic works across our regio's boundary, that also means our aegis works inside it, so it wouldn't really be a bad thing for us.
I just like being able to hide from the big nasty Guernici.