In my opinion, some of those stunts are overpowered. In general, a stunt is supposed to give you 2 shifts of benefit some of the time
"Fast and Deadly Use Athletics for combat rolls, provided you are unarmed or useing a weapon that can be held in one hand."
Basically, what you've done here is collapse four skills into one. With this stunt, there is really no reason to have Fists, Weapons, or Guns. And since Athletics is the default skill for defense, literally every roll for offense and defense is covered by one skill. Ok, you are slightly limited in that rifles and zweihanders aren't covered, but that's a fairly minor consideration. Consider that most skills list 4-6 trappings, thus when a stunt borrows a trapping it should gain about 20% of the utility of the (one) skill it borrows from.
How to fix this? Perhaps something along these lines:
Fast and Deadly: Whan a narration of the character's Weapons attack showcases his athletic prowess, Athletic complements Weapons. Alternately, if the character makes a Weapons attack after making a supplemental move, he can ignore the penalty for the supplemental move action.
With no more than a modest effort, this should allow you to claim a +1 on most of your weapons attack rolls, which is within reason for a stunt. (Note that the second option is only different than the first option in semantics.)
Small Weapons Expert when using a weapon that can be held in one hand, inflict 2 extra stress.
This translates to +2 damage whenever you attack with melee or ranged weapons (since you plan on using only one-handed weapons anyway). It needs to be re-worded to affect only one type of attack skill, and should either give you a +2 bonus *occasionally* or a +1 bonus routinely.
"Trust your Knowledge use Alertness when making Declerarions or Assesments, so long as its something that could have been researched or read up on."
This seems too broadly defined ... and really doesn't make much sense. What does Alertness have to do with memorization of facts, orthe capacity to trust in such knowledge? Based on your description of what you intended for the stunt, perhaps it would make more sense for the stunt to allow you to roll Contacts in place of Lore when performing Arcane Research? (Or mayby Scholarship for Academic research, I wasn't too clear on your wording...)
That's my opinion, at least, others may have different views.