Slats,

I would suggest you run Dailys and use that cash to Buy BoE gear so you can do the Heroics. So much good gear on the AH that you can get in order to increase your dps.

To answer some of your questions.

* What is considered the standard Ele Shaman boxing spec for PvE?

http://elitistjerks.com/f47/t20914-shaman_elemental/

* What is considered the standard Ele Shaman boxing spec for PvP?

http://elitistjerks.com/f79/t39578-elemental_pvp_specs/

* Which Heroics are considered the most boxer friendly and 'easiest' to farm for badges at the beginning?

Imo this is the order for easiest to hardest. (Number represents the badges)

Utgarde Keep: Utgarde Keep (3)
Gundrak (5)
Drak'Tharon Keep (4)
Violet Hold (3)
Azjol-Nerub: Azjol-Nerub (3)
Caverns of Time: The Culling of Stratholme (5)
The Nexus: The Nexus (5)
Utgarde Keep: Utgarde Pinnacle (4)
Azjol-Nerub: Ahn'kahet: The Old Kingdom (5)
The Nexus: The Oculus (4)
Ulduar: Halls of Lightning (4)
Ulduar: Halls of Stone (4)
Trial of the Champion (3)

* What totems do you all drop? Currently using:
(I run 3 Shamans / 1 Priest)

FIRE: 1x Wrath / 2x Searing
WATER: 2x Mana Stream
AIR: 1x Wrath Of Air, 1x Windfury, 1x Grounding
EARTH: 1x Strength, 1x Armor, 1x Tremor

Link to my toons in case this helps
Tank
http://www.wowarmory.com/character-s...Thul&n=Shonkey
Shamans
http://www.wowarmory.com/character-s...7Thul&n=Zebina
http://www.wowarmory.com/character-s...7Thul&n=Xylina
http://www.wowarmory.com/character-s...7Thul&n=Yihana
Priest
http://www.wowarmory.com/character-s...ul&n=Veristine