You most likely cannot apply automatic fire with Throw Back Arrows feat, but X-laser beam still does the same if thrown back
At first, I want to state that those responsible for writing these rules are going to be officially awarded a Malkavian Embrace. Now, to your question.
the feat specifies that bullets are not ranged ammunition
They are ranged ammunition, the feat Throw Back Arrows specifies with which types of ranged ammunition it works and with which it doesn't. The feat is silent on keeping any special types of the attack -- just that it deals full damage, also adding your Strength modifier (for throwing the laser beam especially strongly). I would rule that it does, though, as it is stated as dealing full damage of the projectile, and I would say that special modifiers are a part of that full damage.
And there is an important part:
When using the Snatch Arrows feat, you can throw a caught piece of ranged ammunition
Which, as I understand it, implies "one piece of ranged ammunition", read further to get more evidence for "one piece".
What goes to automatic weapons in general:
Automatic: This weapon can act as a semi-automatic weapon (see below), or it can fire a burst of shots with a single pull of the trigger to attack all creatures in a line. This line starts from any corner of the wielder’s space and extends to the limit of the weapon’s range or until it strikes a barrier it cannot penetrate. When using an automatic weapon to attack all creatures in a line, the wielder makes a separate attack roll against each creature in the line. Each creature in the line can be attacked with only one shot from each burst. Each attack roll takes a -2 penalty, and its damage cannot be modified by precision damage or damage-increasing feats such as Vital Strike. Effects that grant concealment, such as fog or smoke, or the blur, invisibility, or mirror image spells, do not affect an automatic weapon’s line attack. Roll to confirm each attack roll that threatens a critical hit separately. A single burst with an automatic weapon consumes 10 charges. When taking a full-attack action with an automatic weapon, the wielder can fire as many bursts in a round as he has attacks, provided he has enough charges to make all of the attacks.
I would read it as you catching the one piece of ammunition shot at you, and then possibly "throwing" it back, just as Yoda did. However, note that an X-laser fires differently, achieving the effects of automatic fire without actually automatically firing (thus no penalties):
When making an attack with an x-laser, make a single attack roll and compare that result to the ACs of all creatures in a line extending out to the weapon’s maximum range. This weapon damages all targets with an AC equal to or lower than the attack roll.
So, you can catch one ray and damage everyone whose touch AC is lower than your (presumably new) attack roll. Sounds cool!
What goes to automatic laser weapons like the Laser Rifle, presumably, you cannot apply automatic fire, as you only catch one of the rays (the one aimed at you), and automatic fire is not a single strong beam penetrating everything, it is a burst of shots, each shot separately aimed at each target (which is the fact that implies the penalty).
Thanks you for that mind-breaking exercise, it is now 95% that I will play a Monk with Throw Back Arrows if I ever get a chance of playing at that setting.
Can the X-laser ray be considered ammunition?
This is a hard question, but if it is not, even if you deflect it with your hand using the Deflect Arrows feat (as it is "a ranged weapon attack", you can do it), and then snatch the ray for future use with the Snatch Arrows feat, you cannot activate Throw Back Arrows feat, as it only works on "caught piece of ranged ammunition", doesn't work with bullets (but very vaguely defines the class of ammo that it works with, so if we want to talk absurd here, we can).
But what is ammunition? Here is the definition:
Ammunition: Projectile weapons use ammunition: arrows (for bows), bolts (for crossbows), darts (for blowguns), or sling bullets (for slings and halfling sling staves). When using a bow, a character can draw ammunition as a free action; crossbows and slings require an action for reloading (as noted in their descriptions). Generally speaking, ammunition that hits its target is destroyed or rendered useless, while ammunition that misses has a 50% chance of being destroyed or lost. Although they are thrown weapons, shuriken are treated as ammunition for the purposes of drawing them, crafting masterwork or otherwise special versions of them, and what happens to them after they are thrown.
It doesn't list bullets. However, the "Firearms" page has the word "ammunition" repeated 19 times.
So, can we actually say that there is a precise definition of what is ammunition? Unlikely.
One could say that laser beam is not a projectile, and laser rifle is not a projectile weapon.
The we have such an entry on the Technological Weapons page:
Range: This lists the weapon’s range increment; no listing is given for melee weapons that cannot be thrown. Unless otherwise noted, all firearms in this chapter are treated as projectile weapons for the purpose of determining their maximum range.
Are the laser weapons firearms? Yes, many of them have a special entry "exotic (firearms)". This argument, however, can be deflected with the statement that their "projectileness" only applies for "determining their maximum range".
X-laser is listed as "exotic (heavy weaponry)", not as a firearm, so it is possible to claim that it does not count. Or not.
There is some interesting FAQ about the Snatch Arrows combat feat, though:
Update: If the attack is deflected, not only does the target take no damage, but any other effects (ability drain, negative levels, harmful conditions, and so on) associated with that attack do not occur. If the deflected attack is a touch spell or other effect that requires “holding the charge,” the charge is not expended. For example, if a ghoul’s claw attack is deflected, the target is not subject to the ghoul’s paralysis ability from the attack. If a shocking grasp touch attack is deflected, the attacker is still “holding the charge.”
So, if one claims that the laser weapons function on charges (well, they are), we can treat the "charge" as if it would not even be activated.
Then it is possible to claim that as soon as "you don’t take a penalty for throwing a weapon that isn’t designed to be thrown", it will just fire normally now.
However, we have actually came to the point when the wording seems to be ambiguous enough for one single answer to be non-existent.
Using "logic" doesn't help here
Even though catching a ray of X-laser and throwing it back may sound stupidly, we are already talking about Star Wars-esque Fantasy here, and it can be considered cool in this setting. Or not -- up to your taste.