There are lots of threads about the arcane archer's imbue arrow ability but I didn't find one that clarifies whether it works with quickened or immediate action spells.
Is there some FAQ or something about this?
If I am a myrmidarch 4/full bab class 3/Arcane archer 3 can I:
Cast a ray spell, shoot it with my bow with added frost ability then cast a quickened area spell, shoot it with my bow with added frost ability?
Alternatively (if I find any) cast a ray soell, deliver it with the bow, then cast an immediate action range spell to deliver with my bow?
At 2nd level, an arcane archer gains the ability to place an area spell upon an arrow. When the arrow is fired, the spell's area is centered where the arrow lands, even if the spell could normally be centered only on the caster. This ability allows the archer to use the bow's range rather than the spell's range. A spell cast in this way uses its standard casting time and the arcane archer can fire the arrow as part of the casting. The arrow must be fired during the round that the casting is completed or the spell is wasted. If the arrow misses, the spell is wasted.
It states that the spell uses it's standard casting time.
If I am a myrmidarch 4/full bab class 3/Arcane archer 3 can I:
Cast a ray spell, shoot it with my bow with added frost ability then cast a quickened area spell, shoot it with my bow with added frost ability?
You could fire a ray and deliver it with ranged spell-strike with benefits of Enhance Arrow (elemental) and you could theoretically cast a quickened area spell and deliver it with another arrow (in practice described character probably wouldn't be able to cast quickened area spell because he wouldn't have high enough slot for quickened spell and because bow is two-handed weapon he would need a third hand to use rod of quickened spell). However, I think that Imbue Arrow works differently than ranged spell-strike and does not inflict arrow damage (and thus does not add elemental damage) - it seems to me that it only allows using bow's range (which can reach 1000 feet even at low levels - myrmidarch would get -18 penalty to attack roll but targeting a specific square is attack made against AC 5).
Alternatively (if I find any) cast a ray soell, deliver it with the bow, then cast an immediate action range spell to deliver with my bow?
I see no limit on spell-strike or ranged spell-strike how often it can be used so you are limited only by number of ranged touch spells you can cast per round (i.e. one standard action and one swift action).
I have seen others in other threads claim that imbue arrow was at least a standard action. That's why I asked.
I see nothing in its description that would warrant it. Spell-like abilities use standard action if no other casting time is given but Imbue Arrow explicitly states standard casting time of the area spell being fired.