Tyche:
Incite Misfortune (ranged, weaponized etc...)

While it may be a bit nitpicky, I wouldn't use Incite Emotion for this because Misfortune isn't an emotion... and because (if I'm not mistaken, don't have my books handy) when upgraded to Weaponized,  it deals mental or social stress, not physical.

I feel this could be better modeled by as a form of Channeling using "Luck" as an element. If you want to modify it to less resemble mortal spellcasting, I suggest a custom power working the same way but removing the focus items and combining the roles of Conviction and Discipline into one of the two skills... I figure you shouldn't have to adjust the cost that way since adding the trapping from one to the other is basically the same as a one refresh stunt and losing the focus items should refund a refresh since that's what it costs to buy the same amount (again, no books right now) of focus item slots with Refinement for Evocation or Thaumaturgy.

Not really sure about the Naga, but I wanted to make a comment about the Quarin you mentioned. I didn't read Ghoul Goblin, but if you're saying that it can grant sponsored magic, that means that it is Plot Device levels of powerful, so the standard rules for that apply: Anything is should be good at should be at Epic (in this case, since it can sponsor a mortal's magic, I'd guess all spellcasting skills would be Epic), any skill it seems like it wouldn't be really good at is Fair or Average, and anything in between is good or great.

Not what I meant.

My point is, a taser costs no Refresh. And it's electrical. Mjolnir's electrical-ness should likewise be free.

Just because the narrative tags attached to items are free doesn't mean you can swap them out whenever you want. It just means you need not spend Refresh on owning items with them.

Ok, now we are on the same page.

I disagree with the lightning damage being a narrative descriptor that you could get for free. A character with no supernatural power can't say that his baseball bat/bullets/rubber chicken is charged with lightning when he realizes that the iron golem he's fighting is weak to electricity.

Also, yes, you could throw any hammer one zone away for free, but then you have to go get it to use it again. I also give my players leeway on the one zone range for breath weapon because I feel it's a poorly written power (as has been mentioned on this forum before).

Hrm...
Inhuman Strength -2
Supernatural Toughness -4
The Catch () +?
Item of Power - Mjolnir +1
Breath Weapon (Lightning) -2

That's a total of -7 refresh assuming a +0 catch. If you get at least a +1 Catch, he can upgrade to supernatural strength. Also, you could start with supernatural strength and no Mjolnir until later when he learns his identity and the refresh level may have risen.

Note: I went with breath weapon because it's aimed with the Weapons skill and affords better synergy than channeling would. Don't see much need for a custom power here.

First, I agree that skill replacement isn't always the best method of handling thaumaturgy difficulty. As stated, if you do a Resources replacement, a twelve shift ritual could likely get you a nuke, which is overpowered. On the other hand, if you wanted to do a thaumaturgy teleportation like spell and used an Athletics replacement, those same twelve shifts only moving you twelve zones seems underpowered... especially when you consider that wouldn't come close to letting you leave the blast area of the nuke that last fictitious ritual just summoned.

However, in this case, I don't think a skill replacement on Resources is that bad of a gauge. Consider what mundane items would be needed to accomplish the same thing, the drawing of a picture on one device that lets it appear on another device. Seems like a pair of electronic tablets with a 3G connections would fit the bill and you could probably buy two for between $500 and $1,000... putting the difficulty at Fair since a Fair Resources roll would let you buy anything under $1,000.

As I said though, that kind of thing doesn't always work. The big thing to ask yourself anytime you set a difficulty on something is, "Does that sound reasonable in terms of cost and benefits?" Here, it certainly sounds reasonable to me.. you're only putting in a Fair effort and in return you're getting something useful, but not amazing. It will allow the characters to communicate silently and effectively across a distance, but it's not going to win any encounter for them all on it's own. Plus, it requires planning ahead before it's actually used, which always makes a difference to me when I set difficulties (Wanna pick the lock on the exit door before the fight starts to make sure you have a quick way out? Burglary roll of two. Wanna do it while under fire and trying desperately to make an escape? Difficulty just went to five.)

My personal favorite method of accomplishing this is to use a maneuver to place a knocked back aspect on the target and then use one shift per zone that the target is moved. So moving one target one zone is four shifts. Add two shifts to make it zone wide and it's 6 shifts to move all targets in a zone one zone away.