It depends on how many slots you have in the first place. I was thinking of commenting every spells, but I dont know enough of these spells to really comment on each.
However, I do know some (played an oracle, basically the sorcerer version of wizard):
Cant say for 6th level, didn't reach that. I cannot say if they would be a must for every cleric, but they did seem like the most appealing choices when I played my oracle, even if some of these spells are meant to be casted once a day, they were good enough for me to use a spell known slot for that.
Your unarmed attacks would be pooled together for the style, your claws wouldnt, so in the case of the pummeled charge, you wouldn't be able to use your claw attacks in there because it only applies to unarmed. Also, since you use your iterative attack, all your claws become secondary melee attacks (-5 to hit bonus and half strength bonus).
For the question : I would be tempted to say a dazing ball lightning, as dazing rules out many enemies in battle and ball lightning has a very good efficiency.
As for your suggestion, I do believe you are correct.
Also, since you need 3 feats for spell perfection, you may want to get persistent (+2) and intensified (+1). Persistent will make for some nice persistent dazing ball lightning (2 saves per attack, daze for 4 rounds if they fail). The intensified is just for some general intensified fireballs (up to 15d6 for 3rd level spell)
Brilliant energy weapon will counter his AC. Just play an equally high AC character and he lose easily. Also, a simple fighter with a brilliant energy scimitar (allows the use of shield), with improved critical, blinding critical, would destroy him. Since brilliant energy ignores armor/shield, he would have an AC of 15 against you, that is roughly a 19 chances out of 20 to hit him on first hit and very likely the same on the second hit (high chance on other hits still). His character may seem strong, but to say that is the strongest is a laugh.
(Your intention)"use paragon surge"
(Arcane surge text)"are treated as if you possessed any one feat for which you meet the prerequisites"
As for what you are trying to do with new arcana from the arcane bloodline, well FAQ :
As a player of a character optimised in vital strike and having done a battle with extreme luck (not a feat, I was lucky on my dice rolls), I would advice against losing any to-hit bonus. I would (in your place) go for a falchion and aim for either improved critical or a +1 keen falchion.
Your main damage as a barbarian (without going all-in vital striking) is your bonus to damage, which power attack, rage and most importantly crits will boost. With improved crit'ed falchion, you can guarantee a 15 higher will hit, regardless of your hit bonus (useful for the attacks you gain later).
TL;DR No, sacrificing to-hit for damage at a ratio lower than power attack is not worth it.
1) I also suppose they don't stack, I doubt it would make sense for someone to gain 10 listed abilities from beast shape when you reach the highest level
2) Since the beastform gives you "animalistic features", I would say you do not become an animal, and thus would not qualify for the size bonus associated with it. At best, I would see you would be able to have the size bonus of +2 as if using alter self.
Any official answer is welcome, this is just my opinion
Considering how few the sources are, I doubt the DM would accept it.
As for the price, if we follow the general price of everything (Bonus squared * X gold) :
EDIT: forgot to add, technically, making this a slotted magic item would divide the cost by 2, since the cost is twice for slotless, resulting in a 9000gp for a hat of initiative +6, for exemple.
It seemed obvious to me that the orc hornbow's ability to copy effects that affects longbow/shortbow is meant for feats/class features/spells and such, not proficiency.
As such, this racial feature would be relevant to the matter "Weapon Familiarity: Half-orcs are proficient with greataxes and falchions and treat any weapon with the word “orc” in its name as a martial weapon."
Considering the previous racial feature, the only way to be able to use a orc hornbow without EWP is by being a half-orc with martial weapon training or having martial training feat to use the hornbow.
As for the effect, well so long as the feat/feature/spell or whatever can affect both longbow/shortbow, then it also applies to the hornbow for being a bow.
For a bit of context : I recently made a cave druid for a campaign, and I have come under a certain issue, for which I havent found an existing FAQ about :
Considering : "At 10th level, the cave druid can assume the form of a Small or Medium ooze as if using beast shape III, and at 12th level that of a Tiny or Large ooze as if using beast shape IV (treating the ooze as if it were a magical beast without a natural armor bonus). When in ooze form, the cave druid has no discernible anatomy and is immune to poison, sneak attacks, and critical hits."
My Opinion : Considering the only things you lose are extraordinary and supernatural abilities based on race (darkvision as a dwarf as exemple), it would odd to lose the most basic sense of all. The only exemple I have found is the "Sea Anemone, Giant", which is blind and has sightless as EX ability, which is not 'granted' by vermin shape. To add to all of that, the cave druid actually specifies that transforming into an ooze grants me the no poison/sneak/crit, I can still bleed however.
A FAQ/errata would be greatly appreciated, any sort of official clarification really.
Considering the guide line for item pricing is mostly comparing with items from the Ultimate Equipement book, and some formula :
Prices to compare :
"Each day, a cleric can prepare one of the spells from her two domains in that slot"
As for the lesser rod of extend, since invisibility is a level 2 spell, it would work. You are expending a higher level slot for a lower level spell, it doesn't change the spell in any way shape of form. The rod doesn't care about the used spell level, only the original spell level.