Fire Trait Line:
Burning Fire has a 60sec cd in pvp and is therefore most of the time useless -> I'd go with Burning Precision, which gives a 15% percent burning duration and the burning on crit is nice when it happens every once in a while.
As some have already mentioned Smothering Auras is usually the pick -> if you feel that condis aren't that much of a problem skip it
Pyromancer Puissance adds more Might and an explosion when leaving fire attunement, which also applies burning.
I personally prefer Arcane Trait Line over Water.
The reduced Attunment cd alone is enough to prefer this trait in my opinion. I personally run Arcane Restoration, Elemental Lockdown and Evasive Arcana(condi cleanse for water dodge). Once you play with the reduced attunement recharge you can't go back. Also if you swap between Air and any other attunement you have perma swiftness.
Weaver Trait Line
I run the exact same. Some prefer Superior Elements though.
Utilities 8-9 are in my opinion purely based in preference, other options would be Stone Resonance(Stab and Barrier), Glyph of Elemental Power(CC-Break and additional condis depending on attunement), Lightning Flash(sometimes played with dagger offhand for earth5->port on ppl) and Signet of Air(shortest CC-Break cd).
I play Sage amulet and haven't played with Carrion amulet so no idea if it's viable.
Runes are also mostly preference based some alternatives I've seen or used would be Rune of the Forge, Rune of the Weaver(sth I didn't really like, although it sounds nice in theory).