BALANCE:
The class is definitely combat-oriented, given full BAB, proficiencies and the special abilities, which are of course all related to archery. It requires to be an arcane spellcaster, but provides no further spellcasting advancement. It is IMHO a well balanced PrCl, probably as powerful as a core class, but somehow one of the main abilities (Imbue Arrow) does not improve with Arcane Archer levels, and requires levels in a spellcasting class to get better at higher levels; this is a drawback for the AA, but if it had +1 level in spellcasting it would be definitely overpowerful.
Many people have mentioned the problem with Enchant Arrow, which becomes of little utility if someone in the party can cast Greater Magic Weapon on ammunition. Of course, IMHO it's not a problem with Enchant Arrow but rather with Greater Magic Weapon. Easy availability of magic ammunitions in the campaign may tune down the ability as well.
FEATURES:
The PrCl offers several new abilities otherwise unavailable from the core classes: this is definitely what a PrCl should provide, and therefore it is a very good point that the AA gets a new special ability or improvement every level.
Imbue Arrow may occasionally give unprecedented possibilities, but the fact that is it restricted to area spells limits its power. If it let the AA cast e.g. touch spells from a distance (although the arrow would still need a non-touch attack) it would have given many many more new strategic tricks, and I still think the class would be balanced.
Seeker Arrow, Phase Arrow and Death Arrow are cool, and even if they require the right occasion to be useful, they may be of great effect. The limit of 1/day is not a big problem.
FLAVOR/RP:
The class can give IMHO great flavor to a PC or NPC (or a group of NPCs). It could become a good career point for a multiclass archer/spellcaster type, although he would have to manage the strongly reduced spellcasting advancement.
Notice that it is a racial-restricted PrCl. Given the fact that the DM is free to allow such a class for other races in special circumstances (such as a human raised by elves), I personally appreciate the case: I think it can give more flavor for the whole race if the PrCl is e.g. notorious in a setting, and satisfy a player's choice of race.
REQUIREMENTS:
I believe that requirements are one of the most important thing in a PrCl, after all they are what all members of the PrCl share in common (together with the 1st level benefits). Apart the racial restriction said above, the requirements here are very solid with the concept of the Arcane Archer: none of them is in fact a "burned feat" i.e. used as a "cost" to qualify, and - with the exception of at least 1 level in an arcane spellcasting class - they allow any core class to qualify, which is in line with the original ideas about PrCls (or at least the guidelines in the DMG).
DESIGN:
A final comment on design and explanation...
Possibly the proficiency list is a little too good. A single-classed Wizard can qualify, and he would get martial weapons, shields and up to medium armor prof., which IMHO do not necessarily fit with an archery training.
Some issues remain unclear about Imbue Arrow: if the character had also levels as a divine spellcaster, can it be used with divine spells as well? Can (and how) you combine spontaneously cast metamagicked spells with the standard action needed to cast & shoot?
Death spell DC is a constant. It could have been better if it improved with levels. ELH addresses this by introducing an epic feat IIRC that increases the DC every time it is taken.
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OVERALL: 9