FYI this should probably be in the Rules Questions section.
Does that mean that at level 1 I would get whatever feat I want as long as I meat the requirements plus that extra weapon focus feat?
I'd like to confirm that if I do this that my weapon focus claw/bite would act as sacred weapons and start off with dealing 1D6 damage.
Next I am wondering about the damage bonus of my weapons. Say my Tengu Warpriest has 14 Strength. Would all of my natural attacks be 1d20 to hit +2 from my strength. Then say I did hit I would deal 1d6 damage +2 from my strength?
Yes, but your attack bonus would actually be 1d20+3 (+2 strength +1 weapon focus).
So this would make my 2D8 natural sacred weapons be treated as if they were large so they would deal 3D8 damage right?
I would say yes but check with your GM on this one.
Now lets say I have a longsword in 1 hand with my 20 strength and I'm level 20 (weapon focus longsword). Do I still get my natural attacks at full BAB and full strength bonus?
No. When using natural attacks to supplement weapon attacks, they count as secondary attacks. This means -5 to hit and only half strength bonus to damage. Also there's +1 to hit from weapon focus. So in your example it would be longsword +26/21/16 (2d8+10 dmg), claw +16 (3d8+7 dmg), bite +16 (3d8+7 dmg).
Are my Claw, Bite and Gore attacks considered piercing?
Not quite. Claw is bludgeoning/slashing, gore is piercing, bite is bludgeoning/piercing/slashing.
Hit with my Gore weapon tusks. Deal damage. Then make my grapple check from Hamatula Strike. If that succeeds I would deal them 2D8 damage from my armor spikes?
Not as I read it, no. You must make a grapple check as an attack action to deal the extra 2d8 (plus strength etc) damage with your armor spikes.You could then break the grapple as a free action and restart it on subsequent piercing hits, but since you aren't making any grapple checks to deal damage there would be no point.