Have your GM pick an existing avatar that closely fits with your deity's theme I suppose.
Hard to say. As a deity of chaos, I suppose you could even choose randomly. That could be fun.
Otherwise, I would recommend looking at other protean monitor gods.
That's a great idea, lastly,can I cast spells while in Avatar form?
Battle forms do not allow spellcasting, speaking, or most manipulate actions unless specifically stated otherwise in the battle form's spell description.
So no, you can't cast spells in avatar form. You can use your hands though, per its specific description.
You can find the rules for battle forms here, under the Polymorph trait.
No, the rule cited above from Ravingdork says
"Unless otherwise noted, the battle form prevents you from casting spells"
Unless the ability says you can cast spells while in that form, you can't.
You can't even speak in Avatar form because the ability doesn't say you can.
Kelseus is correct.
Oh jeez, that spell is looking horrible now
Most polymorph battle form spells give martial level stats for attack and damage.
The intent of nerfing their spellcasting into nonexistence is so that the game rules don't create a loophole allowing a super-gish - a character that has full martial stats and full spellcasting stats. The battle form spells allow a spellcaster to almost fully switch over to a martial role (they are often still lacking a bit in the HP department), but they fully give up their spellcasting to do it.
I just noticed the spell reads "You have hands in this battle form and can take manipulate actions" would this also mean I can cast all spells?
It means you can perform these actions that are not allowed in other battle forms.
As mentioned, battle forms are intentionally prohibited from casting spells (or using kineticist impulses). However, I believe that a caster can sustain existing spells while in battle form since the Sustain action has just the Concentrate trait.
I also believe a summoner with an eidolon that can cast spells (via Magical Understudy, Magical Adept, and Magical Master) can be a partial workaround to this restriction.
With a few exceptions (like polymorph spells) ongoing spells also continue to function. For example, a wizard could buff themselves with mystic armor, heroism, and invisibility (4th) prior to turning into a fearsome, invisible dragon.