I'm supposed to "focus the crystal" by casting fire and frostbite at it. Well, the tomes available are called "Fire Hands" and "Ice Hands," not sure if a mod did this or what but I can't cast the correct spells at the crystals. Help?

Hm. You dont have a novice level frost spell? thats all you need.

You probably have the Better Sorting mod enabled. This is the one that changes flames to Fire Hands etc.. For the love of Azura read the mod's description when you download it.

Flames(Fire Hands) and Frostbite(Ice Hands) are the two spells needed to focus the rays of light in the correct position.

That is about THE coolest puzzle Bethesda have placed in an ES Game. I had no prior knowledge, but knew what was sort of expected of ES puzzles.

Looked about, placed the focusing, experimented with the spells available in the room, and then experimented with the mirror moving contraption.

it feels really good to figure through one of the puzzles without any clues.
You need to watch the effects from each type of spell, and watch how far the shifts go.

total immersion (and I am a puzzle solver IRL).