right now you have 0 ranger spells, because you're not wise enough to use them...
think about upping Wis to 11 and use your ranger spell(s) for gravity bow.
you won't actually gain any of the arcane bloodline spells (unless there's an FAQ somewhere i haven't seen) because you're not leveling as a sorcerer at all and those aren't covered by the "+1 level of existing class" spells/day bonus that AA gets.
for actual sorc spells... it depends on what you want to do. you can't reliably cast them in armor unless you plan to invest in Arcane Armor feats (and use up swift actions). if you're ok being a glass canon (a fragile damage dealer) drop your armor and focus on spells that increase chance to hit or damage dealt. if you're looking to hold on to some survivability, keep the armor and focus on spells that have no somatic components (like true strike and feather fall), or are utility spells you can cast out of combat (after removing your armor). if you really want to try both, take mithril chainshirt (only 5% ASF) and whatever spells you like.
personally, i would risk the 5% instead of spending a feat to be able to use a swift action to ignore it. YMMV
also, i wouldn't rush into anything combat-caster-related... it'll most likely be a while before you have any spells that are a better option in combat than a full attack with your bow.
You might even want to up your wisdom to 12. It will double the number of ranger spells you can cast at fifth level.
If spell casting is important to you -- you could stop the ranger progression at level 5 and qualify for AA at Ranger5/Sorc 2.
I think your stats aren´t the best, but I doubt you can change that. If you can, more strength and wisdom at the expense of charisma and to a point constitution may be worth it - with so many ranger levels, you can raise Charisma with your level increases and it will be enough.
For feats, Improved Precise Shot and possibly clustered shot can be great if you want to make your archery counts, and that is basically most of what your build has going for it.
Also, at that level you can expect some pretty mean and tough beasties - more damage is always better. Combat casting is for the people who expect to be in melee - and you should definitely look for ways to avoid it :)
do you have to be a half-elf? and how patient are you?
a plumekith (an aasimar variant) gets +2 dex and wis, which is great. and zen archer is super badass; pair it with the empyreal sorcerer and you've got a really solid base, though it does slow down entry a bit... zen archer 4/empyreal sorc 2/ranger 2 would be the fastest (and gets Wis to AC, attack rolls, and as casting stat), it does miss out on ranger spells though... it would probably be better to go zen archer 8/empyreal sorc 2 but then you'd have to wait til 10 for AA
do you have to be a half-elf? and how patient are you?
a plumekith (an aasimar variant) gets +2 dex and wis, which is great. and zen archer is super badass; pair it with the empyreal sorcerer and you've got a really solid base, though it does slow down entry a bit... zen archer 4/empyreal sorc 2/ranger 2 would be the fastest (and gets Wis to AC, attack rolls, and as casting stat), it does miss out on ranger spells though... it would probably be better to go zen archer 8/empyreal sorc 2 but then you'd have to wait til 10 for AA
This is a pretty cool idea. I really like the interaction of AA / Zen Archer / empyreal sorc a lot.
When it comes to ranger you want the 6th level prior to prestiging out for the bonus combat feat.
I would suggest, on a 20 point buy:
STR 15
DEX 16 (18)
CON 12
INT 10
WIS 14
CHA 7
USe Sage Bloodline or go wizard. 6/1 split. drop one point into STR, rest into DEX.
OR, go fighter 5/2 sorcerer. Lower CHA as necessary.