Good piece, but there's something I feel should be tweaked.
In the elementalism part, it wouldn't make much sense for the weapons to materialize the infused element from nowhere. Elementalism has always hinged on the use of pre-existing natural elements, the ice-spear example sounds an awful lot like voidal magic with the spike forming out of nowhere.
For the sake of consistency, a source should be required to draw water from in that type of connection.
The fire sword could be tweaked as well, something like the blade not literally producing visible flames, but heating the metal itself to become red-hot. This would harm the user as well, as gripping such a weapon or tool would burn your hand. Use of gloves to reduce self-damage sounds like an interesting idea to play around, just as long as there's a drawback.