This FAQ doesn't cover SLAs gained from feats or traits. I imagine that they follow in suit to everything else but I can't find an official ruling, so if anyone has a link it would be appreciated.
You can only ever get cantrips and orisions from traits. The distinctions in the traits themselves should be plenty. They are always referred to as "cantrips" or "orisions." These labels should be plenty to distinguish them as arcane and divine.
Nope a good chunk of them (over 30) don't specify, and there are some for spells that are 1st level and above as well (although all of those, like absolute loyalty are all clearly either arcane or divine.
For spell-like abilities gained from a creature's race or type (including PC races), the same rule should apply: the creature's spell-like abilities are presumed to be the sorcerer/wizard versions. If the spell in question is not a sorcerer/wizard spell, then default to cleric, druid, bard, paladin, and ranger, in that order.
For spell-like abiities gained from a class, use the spell type (arcane or divine) of that class to determine whether the spell-like ability is arcane or divine. If the class doesn't cast spells, use the above rule for spell-like abilities from race or type.
Follow the same default list as everything else. I can't see why you would treat feats/traits any differently to race/type/spell-less class.
I definitely would treat them the same and I imagine most DMs would as well, but for my AM SKILLMONKEY build someone pointed out that since Alluring is a religion trait and SKR talked about the intent of the theme of certain SLAs it could argued that as it is tied to religion, it might come off the cleric list instead of the wizard list which would not allow one to use this trait to qualify for arcane strike. That's why I'm looking to find out if there is a concrete answer because otherwise some builds might have table variance on whether they qualify for arcane strike or not (kind of irrelevant for the build I linked to since it doesn't get it until level 13 so would be retired from PFS anyway and my home GM treats them as any other SLAs, but it is relevant for say a bloodrager who wants to take Arcane Strike at first or third level before they can actually cast spells in PFS)
Well, it the case of SLAs that by the rules would be considered arcane, but have a source that could have them considered divine, sadly that is going to have table variance. However, for PFS, there is, to my eyes, ample choices to choose from to assuredly qualify for something such as Arcane Strike if you want to avoid table variance. In general, precedent would say that trait SLAs work the same as any SLAs in determining arcane/divine.
(Also, both Magical Talent and First Memories seem pretty clear in terms of arcane/divine. The first says that you've mastered a cantrip, the second replaces the normal racial SLAs with a variant set.)
To qualify for Arcane Strike, you need to be able to cast arcane spells.
The bonus you get is based on caster level, not arcane caster level.
If Alluring is deemed divine, grab any other trait that grants an arcane spell also. Then you qualify for Arcane Strike, and can do damage off Alluring's scaling caster level.
/cevah