David Thomassen's page

The table on Item Creation gives the cost for "Multiple different abilities" for slotted items as "Multiply lower item cost by 1.5" There is a warning on the webpage Altering Existing Items warning against moving powers from one slot to another, especially inappropriate locations.
As with all things non-PFS it is up to the GM to say, but expect the price to be 50% higher than the head slot, remembering that normally you can only purchase even bonuses to stats (+2, +4 or +6)

Once engulfed by the Cube there would be no line of effect to cast the spell on the barbarian.

The wording appears to work only for manufactured weapons Double Slice
"Benefit: Add your Strength bonus to damage rolls made with your off-hand weapon.
Normal: You normally add only half of your Strength modifier to damage rolls made with a weapon wielded in your off-hand."
It also has a prereq of "Two-Weapon Fighting" (Not Multiweapon Fighting)

Quilted Cloth "This enhanced form of padded armor has internal layers specifically designed to trap arrows, bolts, darts, shuriken, thrown daggers, and other small ranged piercing weapons. When these kinds of weapons strike you, they tend to become snagged in these layers and fail to harm you.

Benefit: You gain DR 3/— against attacks of this kind (small piercing weapons). The special layers of the armor have no effect on other kinds of weapons."

So yes, it does work, as the bullet is a small ranged piercing weapon.

Natural Attacks (Bestiary)
"Creatures with natural attacks and attacks made with weapons can use both as part of a full attack action (although often a creature must forgo one natural attack for each weapon clutched in that limb, be it a claw, tentacle, or slam). Such creatures attack with their weapons normally but treat all of their natural attacks as secondary attacks during that attack, regardless of the attack's original type"
Bestiary rules > Core Rule Book in this case

Tiny and Large Weapons
Improved Natural Attacks
Damage dice increase as follows: 1d2, 1d3, 1d4, 1d6, 1d8, 2d6, 3d6, 4d6, 6d6, 8d6, 12d6.
1d10 points of damage increases as follows: 1d10, 2d8, 3d8, 4d8, 6d8, 8d8, 12d8.

(So 1d8 goes to 2d6 goes to 4d6, not 3d8 - for x9ss)
Got to love ninjas

James Jacobs on this
"Nothing's changed here, really. Jumping is a part of movement. If you're charging and part of that charge needs to be a jump, that's fine. You'll just need to make the appropriate Acrobatics DC to make the jump; if you fail the jump, obviously your charge is wasted.
"
So you can jump as part of your movement to avoid difficult terrain - jumping over an ally would require an impressive high jump

I believe that it has been stated on this forum already (will put a link here when I find it) that Augment Summoning does not work (in general) will summoning Spell Like Abilities, (The Summoners Summon Monster being the exception, but this has not hit the FAQ for the APG).
The Feat does work with the Summon Eidolon as that is a "Summon" spell.
I can see where you are coming from for the Feat to work with the Eidolon, but I believe that it would make the Eidolon too powerful.

Making an Attack of Opportunity: An attack of opportunity is a single melee attack, and most characters can only make one per round. You don't have to make an attack of opportunity if you don't want to. You make your attack of opportunity at your normal attack bonus, even if you've already attacked in the round.

An attack of opportunity “interrupts” the normal flow of actions in the round. If an attack of opportunity is provoked, immediately resolve the attack of opportunity, then continue with the next character's turn (or complete the current turn, if the attack of opportunity was provoked in the midst of a character's turn).

Combat Reflexes and Additional Attacks of Opportunity: If you have the Combat Reflexes feat, you can add your Dexterity modifier to the number of attacks of opportunity you can make in a round. This feat does not let you make more than one attack for a given opportunity, but if the same opponent provokes two attacks of opportunity from you, you could make two separate attacks of opportunity (since each one represents a different opportunity). Moving out of more than one square threatened by the same opponent in the same round doesn't count as more than one opportunity for that opponent. All these attacks are at your full normal attack bonus.

I believe that you can make only 1 attack of Opportunity due to the movement of a character through threatened squares, but you can decide (as they leave each threatened square) when you want to make that attack.

Metamagic rods hold the essence of a metamagic feat, allowing the user to apply metamagic effects to spells as they are cast. This does not change the spell slot of the altered spell. All the rods described here are use-activated (but casting spells in a threatened area still draws an attack of opportunity). A caster may only use one metamagic rod on any given spell, but it is permissible to combine a rod with metamagic feats possessed by the rod's wielder. In this case, only the feats possessed by the wielder adjust the spell slot of the spell being cast.

Possession of a metamagic rod does not confer the associated feat on the owner, only the ability to use the given feat a specified number of times per day. A sorcerer still must take a full-round action when using a metamagic rod, just as if using a metamagic feat he possesses (except for quicken metamagic rods, which can be used as a swift action).

So no for Spell Level increase, Yes for time change

The only time that Caster Level is a pre-req is when its listed in the requirements section or the item being created is a weapon or armour. (For straight '+' only)

Core RuleBook Faq