The balance of this character is both wildly over-tuned in some areas, and drastically weak in others. It's one of the strangest things I've ever seen. For reference, I completed up to Ascension 6, going infinite with incredible ease every time. I then completed three Ascension 20 runs as custom runs, with no other alterations, and was still able to clear with extreme ease, Heart included. I'll focus my attention on each school at a time because each is drastically varied in terms of power level.

First and foremost, Frost is completely and utterly broken, way, WAY too strong. Freeze as a mechanic is literally Stun, a status effect so powerful there are no cards in the base game which can cause it. And for good reason: it trivializes the game. All freeze effects, if they are to remain in the game, need to both increase in cost AND exhaust after use. The idea that they can only work every other turn is also worth considering in addition to the other changes. It cannot be overstated how powerful that mechanic is. Honestly, it probably makes more sense to just rework the mechanic entirely to something that lowers damage by a flat amount or something. Not as original, but would be much more fair. Also, Frozen Clone is a broken card. It just gives you block equal to the damage the enemy is dealing, and when upgraded, it can do this for free. Yes it doesn't work if the enemy is dealing multiple hits, but often enough it is a 0 energy Intangible. If it also exhausted, it would still be good, but probably fair.

But then on the other side, most fire spells are worse than useless. For meager damage, you are burdened with increasing numbers of Burn statuses being added to your deck. Even if you only received one Burn, I would never play that card under basically any circumstance, and some fire spells can give you MULTIPLE burns. To put this in perspective, Ironclad has a card that adds one Burn to your deck, Immolate. It is an extremely niche card that you rarely want to pick, but it is WAY better than any of these fire spells by a huge margin. You could basically fix fire instantly by removing the burn side effect, and possibly lowering the damage modestly, though even then, the damage was never insane to begin with.

Arcane is mostly fine, basically functioning similarly to the Silent. The one exception is in the card draw department, where they are drastically over-tuned. In the real game of Hearthstone, Spring Water draws only 2 cards, and that should be true here as well. Currently Spring Water draws 5 (!!) cards, and refunds you energy for playing it. Lower the cost to 2 un-upgraded, drawing 2 cards, and then have it upgrade to only 1 energy, and it should be fine, and make infinites much harder to achieve. Same for Book of Specters, which draws 5, and could be set to 3.

I would say that damage numbers are OK, though if the balance changes I am suggesting are implemented, some cards might have to get buffed in terms of damage. I also need to comment on one more specific card, and at least one of the new relics. Wish is the card in question, and it is way too good. You literally get to pick ANY card you want, and play it for free. That's outrageous. It should offer you three choices like most cards, or if you really want to push it, make it choose from all rare cards only. As it stands, it's too powerful not to choose every time if offered. Finally, the one relic that I need to comment on is Robes of Gaudiness. This relic is literally the curse, Normality, and it's offered as a BOSS relic. If I started a run and chose to replace my starer relic with a random boss relic (a very good option because the starter relic is extremely bad), and I got Robes of Gaudiness, I'd just abandon on the spot. Imagine trying to play with a permanent Normality effect. It is my honest opinion that it should just be scrapped. It's not salvageable from a design standpoint, and will only ever doom a run.

I like the idea of this character, but if it's going to be fun to play more consistently, it needs drastic work. Best of luck.