That's correct! A sword arm would be more feasible as an event gain as there wouldn't be a spell anyone could teach her to do the same thing.

She could actually learn a spell that shoots small magic projectiles if you would like to simulate a firearm! It wouldn't be as powerful and more akin to firing rapid darts, but could give her some range.

Yes, sharpening eyesight and hearing could be possible. Hunters would be able to teach her enhanced hearing while anyone who works with small instruments such as a jeweler could teach her enhanced sight. Depending on the strength and how long it lasts, it may take her time to master.