I think this is where Room and Group differ. You know the limit of the Room but have no clue as to the limit of the Group. In the same way you can Target an Individual even if you only see his hand. But that's a whole discussion.
What new level 5 spells?
Not new per se, but...
I'd consider changing the guideline such that it cannot remove fatigue if the target would be below tired, dazed or unconscious, or the equivalent if wounded after the spell is cast. Or allow a stamina roll to ignore the fatigue from cold, or both.
Your right, the spell/effect is too powerful, but I think it might be a problem with the guideline, more than the fact that a low level spell can penetrate more easily.
And my feeling on Multiple casting mastery has been shared elsewhere, and I lean towards believing it should be purchased multiple times for more than one copy.
Yeah, Snap of Awakening counters The Call to Slumber completely. Where's the counter to Fatigue? Doesn't that deserves an extra base magnitude? Or should it count as Deprivation?
Well, going further the PeCo guideline that removes fatigue is Base 10, while the equivalent PeIg guideline is Base 4?
I'm eve more conservative now. The PeIg should only make the person winded due to shivering, and if they are at that level, nothing else..
Ther is no Hermetic method to restore fatigue, although there is a spell that can swap fatigue levels between people... The Call to Slumber, IMO will put someone asleep, but they wil wake up right away, might take them out of action for a round or two, but if someone removes 5 fatigue levels your out for nearly 3 hours. More than five, add another hour for each level beyond five.
A sleep spell variant with a Duration other than momentary should put the target asleep for that Duration.
Loss of fatigue won't actually kill your opponent though, and certain sorts of opponents are invulnerable to Fatigue loss (faeries, animated barn doors, etc). So, it is inferior to a CrIg Pilum of Fire style-effect from that perspective. Not to mention that to rapidly knock someone out with Fatigue loss, the target needs to either already be fatigued, or the caster needs to have sunk many XP into mastering the PeIg effect. Also the caster also needs to be able to cast a suitably sized Intangible Tunnel with sufficient penetration, and have an Arcane Connection to the target. Having the Arcane Connection admittedly makes Penetrating easier --- but it would also make Penetrating with Pilum of Fire easier.
As far as countering lack of consciousness:
Note that one of the mental states that InMe allows you to sense is consciousness. So, possibly one of the mental states that you can manipulate with ReMe is consciousness. Although, quite what it would mean to become conscious without recovering the corresponding Fatigue levels is undefined.
There is also a ReCo 10 guideline that "eliminates the penalties of Fatigue".
Finally, although there is no explicit guideline, if a PeIg effect can remove Fatigue levels, then it would seem reasonable that a corresponding CrIg effect could restore those Fatigue levels.
Being pedantic here, then it is level 15 or 20 spell, and it's a bit harder to penetrate.
Sure, but the underlying issue is that you can effectively remove someone from combat by removing all their fatigue and then send a mundane you have stationed nearby to slit their throat while they are knocked out. And you completely ignored my comparison to the PeCo guideline being Base 10.
Requires being conscious, or that a nearby ally is and either one of them has those spells.
except, I believe it is stated explicitly that Hermetic magic cannot restore fatigue. I'd have to find it, but I know it was mentioned. If your guideline existed magi would fatigue themselves and then cast that CrIg spell to restore fatigue. Or CrCo, if it exists there.
Lift the dangling puppet will neutralize most phisical treats (all the ones with no missile weapons) just by levitating them a foot out of the ground. Upside down for better effect. Multicasting that one is quite effective. Fighting with no support points is quite difficult.
Hermetic magic cannot restore fatigue but can transfer it between recipients without problems. So you can be a fatigue vampire easily. Effective combat method as well, but requires quite a higher casting total.
Chilling you 5 times in the same row chills you 1 time IMS. It is thesame as assuming that an Attack roll is a single hit: not necessarily. So you can chill someone (PeIg) and remove a fatigue level, but you cannot render them unconscius with 5 multicasts. That will make them shudder, and that will be it. Common sense before rules, please. Yes, even talking about magic. YSMV, but this trick was raised IMS and was beaten down by the troupe's uproar. 
I do not buy Richard's argument of the DEO Group cast through an intangible tunnel (AC to grog) not affecting the demons since it is a spell that affects the whole group, not just the grog. The demons will scream in pain while the grog smiles (or is worried, if he is in league with the demons). The target of the DEO is the whole group, not the grog that allowed you to canalize it to the group. Again YSMV, but I think the rules support my stand here (serf's parma).
Xavi
Difficult but not impossible. Fighting while unconscious is impossible. 
Yeah, transferring fatigue can be done, but if the flavor text has any meaning, then I don't think you can be a fatigue vampire, and the wording of the guideline should be adjusted to reflect the flavor text of the spell it exemplifies. The Gif of Vigor is a 20th level spell, and based on the wording, it gives your energy to someone who is less fatigued than you are. Also the wording indicates that this spell is the closest that the Order has come to being able to "restore" fatigue.
I don't have a problem with your house rule. I have a problem with the 5th repeated casting of the 5th level spell knocking out the opposing magus. Whether it comes from a long drawn out combat or because multiple magi gang up on a single magus, a spell that can easily knock an opponent out is really a pretty deadly spell. As I said, it chills, and it should remove 1 fatigue level, it shouldn't remove more than one, IMO. If you want to go below winded, you need to go to the PeCo guideline, which is significantly harder.
I do buy that, it's an invalid target. You can't target a grog, with a spell that targets demons, because the grog is not a demon. IF the connection is to him, the target should be invalid. If it's an AC to the group something that exemplifies a cabal or some other meaningful relationship between the grog and the demons, sure. But just to the grog, like a lock of his hair? No. His uniform, or some other insignia representing the group? Yeah, I can see that.
it is not an invalid target. I can cast a DEO at my chair (I am fairly sure it is no demonic). t will have no effect, but that does not mean I cannot target it by it.
In this case the target is the group of characters the grog is part of. he will be unaffected, but the other will be. If none of them were demons, the target would still be valid 8and I would have to check for botch if I rolled a 0) even if the spell would have no effect if cast successfully.
The grog is still an individual target that is part of a group. You can target the group through him. You need to be aware that thereis a group with him, bbut it is the same as casting a Group spell at a single individual. it can be done, even if it is less efficient than casting the same spell with an Individual target.
Xavi
Yes, it is a Hermetic limit.
Perhaps a CrIg effect that "removed the Fatigue penalties" caused by PeIg would be a better way to express it.
No, because those Fatigue levels wouldn't have been lost due to chilling, therefore the effect of that loss should not be counterable (in some way, not necessarially "restored") by warming.
No, the target is a group of demons, and the grog is not a member of the group of demons --- because he isn't a demon.
If you were casting a Voice range, Group target Demon's Eternal Obivion at an apparent "group" in a field which consisted of two demons and a grog, then there would be no problem. The demons would be affected (assuming penetration), and the grog wouldn't (because he is not a member of the group of demons).
However, in this case we are considering casting the Group target Demon's Eternal Oblivion down an Intangible Tunnel. If the Tunnel terminates at the grog, then the Tunnel does not terminate in a group of demons. The Intangible Tunnel creates the problem.
That would imply that you NEED to KNOW that the group of formed by demons in order to cast the spell. That is not the case. You can cast DEO at a group of chairs for that matter, or a group of trees, even if none is a demon at all. It simply will not affect them if they are no demons, but that does not prevent you from targeting the group. As long as you are using a T:Group spell (DEO) and the target is part of a group you can target it with it, and all the members of the group that can be affected will be.
Xavi
No it doesn't. You can cast it fine, on whatever you like. It just doesn't work unless what you cast it on is a valid target.
You are missing the point that the Intangible Tunnel requires the terminus of the tunnel to be the target of the spell. A Group variant DEO targets a group of demons. If the tunnel terminates in a grog, then it does not terminate in a group of demons. The caster of the tunnel is not within "Touch" range of a group of demons. The tunnel certainly terminates near a group of demons, if there are demons standing near the grog. But that is not good enough to affect something down an Intangible Tunnel.