@Kat
While I do have answers to all those questions (which I will put in spoilers), I'll give up trying to defend my magic and admit that it's not fit for casual rping.
Spoiler
All cast magic comes from the caster's own personal pool of mana, which would regenerate normally or by drinking a potion. Fire can be created by either gathering the heat in the air until it combusts and supplementing mana for fuel or by using tools, the most common type would be a rune, fire essence that has been sealed into a stone, a crystal would be more efficient for a rune. Ice projectiles could be created by accumulating the frost that has accumulated on surfaces or by collecting the water vapor in the air until a sufficiently large piece of ice is formed. Using this same type of manipulation, the caster would be able to launch projectiles.
While tearing something apart would technically be possible, the opposing party's own magic would function as a sort of barrier against any attacking force, significantly reducing its effect. That's not to say that if a mage were strong enough, ripping something apart would be possible at the cost of an extremely large amount of mana and energy on their part. Barrier charms, of physical, magical, and mental varieties, also help against such.
Everything leaks magic around itself, creating an aura, the stronger the being is, the more oppressive it is to anything else within the aura. The ice sprite, or elemental, in question has an aura made of mainly frost magic, creating a mostly permanent bubble of cold around it, this aura would weaken as its mana pool drains. A sprite, however, is the third tier of fairy, which are basically embodiments of nature and, by extension, magic itself so it would have a near infinite pool of mana. Fairies are the absolute weakest beings in the magical world, the sprites are significantly stronger, but are still only slightly above the strength of a novice mage.
No, I did not pull this out of my ass, I have an actual system worked out.