Fire, creates an inferno once landed, envelops a 10 foot radius completely, and tends to be ~1500-2000 degrees Fahrenheit 
Ice, freezes all creatures within a radius of 10 feet for about 15 seconds at -130 degrees celsius (-202 fahrenheit). Can be combined with Water magic to create a hailstorm, which spans a 20 foot radius, and constantly drops grapefruit sized hail for a half a minute.
Earth, creates a large bog of mud in a 30 foot radius, slowing all who walk through it. Lasts for about a minute. 
Wind, create (Very powerful) random gusts of wind in a 10 foot radius strong enough to knock over a fully grown elephant. Lasts for half a minute. Can be combined with Water magic to create a Windstorm, spanning a 30 foot radius, and sending out winds about half as strong for half a minute.
Sun, blind all (Excluding Anthony) in a 20 foot radius for 15 second. 
Moon, cause a large hallucination that appears different for each champion. It is of whatever each specific champion fears most. Lasts for half a minute.
Lightning, summon a lightning bolt that hits where the arrow landed with ~.5 mil. volts of electricity. Can be combined with Water magic to create a thunderstorm, which sends a strike of lightning to the nearest piece of conductive material every 10 seconds, striking it with ~.4 mil volts, and lasts for 30 seconds. (Reduced voltage and time it lasts, maybe thats good... or... bad enough for an auto-hit?)
Rain, a rainstorm begins in the arena. The storm lasts for a full minute, and constantly drops 50 gallons of water per second in a 50 foot radius.

-snip-

I only copied over the magics, since that seems to be the only thing needing editing. Lowered temp. for ice arrow and edited lightning storm.