1. Looking at the transmutation part do I qualify for beast shape 2 at this point ie at eighth level all be it for one round.
No. Class abilities refer to class levels, not total character levels.
Change Shape (Sp) is gained at Wizard level 8.
2. can you once you qualify imbue arrows using a ring of spell storing again as long as spell is permitted.
Imbue Arrow (Sp): "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."
Ring of Spell Storing, Minor: "A minor ring of spell storing contains up to three levels of spells (either divine or arcane, or even a mix of both spell types) that the wearer can cast."
Normally, activating a magic item is not casting, but I think the ring specifically says cast, so I would allow it. Ask your GM to be sure.
Arcane archer raises you spell casting abilities though I am not sure if you get up to lvl 8. The big problem is getting spells. Your increase to spell casting does notgive you extra spells to your arsenal unless you spontaneously cast.
I am looking at the same type of build using a flyer and sorceror for my arcane class.
Your increase to spell casting does notgive you extra spells to your arsenal unless you spontaneously cast.
You don't get the two free spells known per level. Scribing new spells is cheap, even paying to borrow a spellbook while in town.
With seven levels of spellcasting gained from Arcane Archer, with a level 1 wizard to start, that means you miss out on learning the following:
2x 1st-level spells (30 gp to borrow and scribe)
4x 2nd-level spells (240 gp)
4x 3rd-level spells (549 gp)
4x 4th-level spells (960 gp)
Meaning at level 17 you would have needed to spend 1,779 gp more than if you had learned those spells for free.
-edit- This is assuming you have semi-regular access to a small city at the high end.
Not allowing a wizard to get 2 spells per level when taking a prestige class is usually just an inconvenience. So much so that it is just annoying and doesn't add anything to the game. For that reason it is a common house rule to just allow the wizard to get his 2 free spells when he levels and move on.