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Fire Bolt will be harder to level...
Damn, I must have missed some training, never seen that spell before.
Anyway, about the spec for you Skribs, Frost gets much more effective when you hit higher end talents which can really boost the damage output of frost. Double crit damage (Ice shards) increased chance of crit by 50% when frozen (Shatter) + Stacking extra crit% chance (Winters Chill)+ An instant cast, triple damage against frozen targets spell (Ice lance) + A really nice Oh Sh*t button when your important spells are resisted (Coldsnap) = some pretty nice PvE/PvP damage. Although for a leveling spec, I have always loved fire for my mage. Since I play a hunter as my main, all I know is pure DPS. Frost mages as you said have great slowing/freezing effects and have good longevity in battlegrounds.
Also, for me fire hasn't really got the boom boom drink, boom boom drink effect. As long as you effecient with your mana and arn't throwing down flamestrikes and hefty mana spells you should be fine. Scorch is a great mana-per-damage spell as its quick and really low mana.
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Try fire spec with pulling with a regular Frostbolt for the slow effect followed up by Improved Fire Ball... perhaps that will float your boat.
Although it may work, when deep enough fire for imp. Fireball, the damage you could put out with a Pyroblast pull would be much more beneficial to your damage as Pyroblast has a pretty cheap mana cost and gets the increased damage by 10% from Fire Power with also all the crit chance/ ignite powers to it.
So to straight up answer your questions:
1. That would all depend on the depth of your mana pool. If you have a quite large mana pool, then blowing your enemy to bits then a quick drink will keep you sustained for quite a while(Fire). If you have a smaller (but not substantially) one or choose a little more Stamina or spirit above Intellect, then frost would be good. But with both their talents, arcane has better mana efficiency over both of them.
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What I want to do for levelling is to simply nuke a target down before they get to me. I'm assuming fire would be good at this, as I can simply pyroblast and then spam fireball until they die.
Nuking down a target before it gets to you or really quicky would mean you would want a nice Pyroblast crit + Fireball crit + powerful Ignite DoT's to beat it for fire. For frost, some really good Frostbolt crits would be nice, but alas, we cannot pick when to crit. From my experiences, fire would always outdamage frost at those levels as long as both mages had even gear/exerience. Frost gets some really nice damage buffs to it at the later tiers of the tree to start closing in on fire, but you wont be maxing all those talents out at 30-50. So for a straight answer, you will get in melee range unless you get some lucky crits with either spec or you do some good frost/ Slowing with Blast wave kiting. The fights length again depends on how well your pulls go, but on the field, they will probly be longer than the ones you fight at the teen levels, but not by very long. So for a seriously straight answer, neither tree will nuke down you opponent before they get to you on a very regular basis. So you should pick a tree you would feel more comfortable in.
Fire = Kills by face-melting.
Frost = Great tricks with freezing and elemental, but less face-melting, more face-freezing the breaking that face with a Shatter crit.
All in all, it comes down to what would would prefer, Face-melting or face-freezing. Enjoy!