Blood Crow Strike
School evocation [fire]; Level cleric/oracle 4
Casting Time 1 round Components V, S
Range medium (100 ft. + 10 ft./level) Target one creature Duration
instantaneous Saving Throw none; Spell resistance yes
Your unarmed strikes release blasts of energy in the form of bolts of
fire or glowing red crows, which fly instantaneously to strike your
target. You can make unarmed strike or flurry of blows attacks against
the target as if it were in your threatened area; each successful
attack deals damage as if you had hit it with your unarmed strike,
except half the damage is fire and half is negative energy (this
negative energy does not heal undead). For example, if you are a
14th-level monk, you can use a flurry of blows to attack five times,
creating one energy crow for each successful attack against the
target, and dealing 2d6 points of damage (plus appropriate unarmed
strike modifiers) with each crow.
In combat, after you cast this spell, you can then make unarmed strike and Flurry of Blows attacks on the target as if the target were in your threatened area. In other words, everything else remains exactly the same, as long as you are making an unarmed strike or using Flurry of Blows. It does not allow you to, say, make a "flurry of trips", but you may use it to take a Flurry of Blows action with a monk weapon.
Based on the following line from the Stunning Fist feat:
You may attempt a stunning attack once per day for every four levels you have attained (but see Special), and no more than once per round.
A stunning attack is a separate kind of attack from an unarmed strike. Therefore, no, you cannot attempt a stunning strike through Blood Crow Strike. The same goes for Mantis Style.
Amulet of Mighty Fists (+1, Speed)
According to the Speed special weapon property, it applies on a full attack action. According to the following line from Monk under Flurry of Blows, a Flurry of Blows is a type of full attack action:
Starting at 1st level, a monk can make a flurry of blows as a full-attack action.
Therefore, Speed works and grants an additional attack via Blood Crow Strike.
Medusa's Wrath uses the phrasing "full attack action" and "unarmed strike" throughout, see above for how "full attack action" is the same as "flurry of blows", therefore if the opponent meets the prerequisites for Medusa's Wrath to happen, you will get the extra two attacks.
Yes but No
Pummeling Style does work with "full attack actions" and "unarmed strikes", but it specifies DR, not energy resistance. Therefore, it will successfully bypass DR on an ability that already does.
The above is, of course, RAW. As a GM, I might be a bit more permissive with this 4th-level spell, requiring a minimum caster level of 7, plus monk levels just to make worth the trouble. That said, I also would not have made it a 4th-level spell. As an archetype, though... looks off into the sky, thoughtfully considering a ranged variant of an elemental monk...