The fact that Taric is the only practitioner of gem magic is true, but he's not the only one who can use gems for magical purposes - as you can see, there are crystals of all sorts in the League's item lineup, Taric is just the only one with such extensive knowledge of them. He can use -just- gems to fight, unlike other people who use gems as support.
Ashe is an ice magic user, just like Sejuani. Ashe's arrows, if you look closer, are made of ice, just like her bow, and ice is just crystallized water. Whenever she may find herself in need of arrows, she can simply make more out of any nearby water source, or out of air moisture, provided that air is damp enough. ECA is just an empowered version of her normal arrow - when it fires, it encases itself in a large ice form which bursts on impact, damaging and freezing nearby people.