tagging rule goes like this...
you will gain your portion of the gold from the creep if either of these two things is true:
1) you have dealt at least 25% of the total damage to the creep
2) you delivered the killing blow to the creep
gold is split evenly among all eligible Demigods within range (its a large range, like 30 range units at least). the amount of gold each creep carries is based on what type of creep it is. very good info on this stuff can be found here: http://www.gamereplays.org/demigod/portals.php?show=page&name=demigod-economy-gold-guide
regarding the difference in farming efficiency between Fire and Ice TB, there's not much of one. Ice will farm creeps with Rain of Ice. Fire will do it with Circle of Fire or Fire Nova. Either build can nuke a whole creep wave with one shot and have their farming ability ready for use again by the time the next creep wave shows up.
total value of creeps for farming
minotaur 5x4 = 20
archer 2x8 = 16
basic creep wave is worth 36 gold
priests 3x33 = 99 gold
angels 2x66 = 132 gold
catas 2x66 = 132 gold
giants 2x100 =200 gold
so you can see why people hesitate to buy those creep upgrades. the upgraded creeps give MUCH MUCH MUCH more gold when farmed than the basic creeps.