I love card games! I can appreciate someone working on designs from a physical perspective. Here's my feedback in no particular order.
[Rules]
When you play a Book, you will pay the Mana cost, and then place the card face up in front of you. On your next turn, you will read the first Passage. On the turn after that, you will read the second Passage, and so on. After reading the fourth Passage, its effect will activate, and then you will discard that Book face up into your discard pile.
Since you have a physical card game, you need to think about keeping track of the state of cards. I'm not going to explain the entire issue, as you can work it out yourself, but you need to have a “read passage” counter token players can use on books to keep track of their state. It could be as simple as having a dice that you turn to represent the passage index, or 1 token = 1 passage read. Otherwise, relying on player memory is going to be a negative aspect to that system in practice. The same can be true of machines and a few other places.
The player with the longest facial hair goes first. If neither player has facial hair, the player with the longest head hair goes first.
This is one of two really cringy rules I read in the document. In today's social climate, you have to avoid things like this. I'm not going to lecture you or stand on a soap box, but please make a game specific system instead. You can have something as simple as players drawing cards and whoever has the larger mana cost card goes first, or include dice, but make it something involving "luck" relevant to your game.
To end your turn, say “the better Wizard passes play to the worser Wizard.” Or you can just say “I’m done.” I guess it’s up to you.
This is the second cringy rule I read, but less egregious than the first. It's your game, and your rules, so please clearly define an end turn mechanic that is going to be consistent and not cause any issues between players. Consider one day your game is successful and is being played by a lot of people in a tournament style like MtG. I'm not a fan of “I'm done” personally, for the same reason I mentioned about the “game state” in the book stuff, and that's there needs to be a physical state representation of whose turn it is.
I get your good natured humor about the better wizard part, but if I'm a competitive player and my opponent is a competitive player, and we're not friends, and I'm crushing them, and I'm ending my turn by essentially continuing to rub it in, your rules are creating extra friction in a physical environment for no reason other than you thought your game was going to be played by friends who can joke with each other.
When you play a Trap card, you will pay the Mana cost, and lay the card face down in front of you. After your opponent makes whatever actions is described on the Trap, you will reveal it, and activate its effect. Be sure to remember what activates your Trap so that you can spring your Trap at the right time.
Once again, relying on player memory is going to negatively affect that system. Unlike books, I can have up to 5 copies of a single trap in my deck, and while there are only 3 unique trap cards at the moment, I assume that's eventually going to change. There's no reason for this system to exist as it is, because it leads to rules discrepancies between real people by design.
If I'm a loud, aggressive, intimidating player, and my opponent is soft spoken, timid, and avoids confrontation, I can play my 4 cards in a turn, and “bully” them into not letting them play their traps because I've played my cards before they physically stopped me, and once my actions are done, your rules do not allow them to retroactively activate.
Your trap system needs to change to be a dedicated phase of the game, where if there are any traps on the field for a player, whenever an opponent performs an action, the player will then check their traps to see if they have any that can activate.
However, this leads to a problem in itself, what if I have an Absorption Trap, and you're attacking me for 1 damage, but I don't want to waste the trap on 1 damage? I could pass on activating any traps, then say your next spell is going to do 10 damage, and block that one instead. This type of rules ambiguity is going to lead to all sorts of gamesmanship where I could “forget” I had a trap played, only to remember the next turn and use it.
There's some creative ways you can avoid this without causing too much inconvenience, but you can work out a system on your own. My point to you is just that you need to consider things like this.
Finally, you make no mention of trap ordering and activation limits. If I play a Arcane Trap followed by a Mirror Trap, the rules do not state which activates first (could be first in first out, or last in first out). In addition, it doesn't clarify if only 1 trap can activate per action or not. Your rules should ideally leave no room for any “assumptions”!
There is no limit to how much Mana you can store, how many Sparks you can store, or how many cards you can hold in your hand.
I feel that no hand size limit is a bad thing in your design. Making your opponent draw cards in an attempt to “burn” them like you would in HS, given the fact if you draw all your cards you lose your game, isn't a viable strategy, so the lack of hand size management is a negative. But I do understand with the way your cards are, there's a good chance you have nothing to play for several rounds, so that's another issue to solve.
When you play a Gate, you will pay its Mana cost, and lay it face up in front of you. Its effect will remain in use until that Gate is destroyed.
You make no mention about “gate stacking” or “gate play limits” that I saw. If I had 2 Waygates in play, do I get 2 extra turns, for example?
I don't like the current design of gates though, they seem too powerful on paper for virtually no downside. My knee-jerk reaction fix is to require them to have a higher mana activation cost, and then a lower mana upkeep cost, so you pay the mana upkeep cost each turn (after activation) if you want the effect to stay enabled. If you choose to not pay the upkeep cost, the activation cost must be paid again in full to start a new cycle of mana upkeep cost.
At the beginning of each player’s turn, they will draw two (2) cards from the top of their deck. The player who goes first will not draw any cards on their first turn. Then, they will gain three (3) Mana, which you will track on the blue dial.
With no “minions”, and no real “board control” or “tempo” mechanics, I'm not so sure this makes sense. The player going first has 2 less cards to work with, but there's no “advantage” to be had by going first with only 3 mana and 4 cards. I get what you're trying to do, balance going first and second, but I don't think this is really a solution because there's no real early game advantage by design yet.
[Cards]
Since this is an early draft, there's no real point in trying to comment on the balance of everything, but rather focus on the core design being presented. There's a few cards like “Regenerative Burst” that costs 3 and heals 10, yet Breath of Ahn'kiat costs 17 and heals 20. The cost of card draw does not make up for the mana differences. I won't point out issues like those, because they are minor and don't affect the core problems with the design.
Just reading over your cards, my initial thought was “a lot of these books/gates just don't sound fair”. I feel the design is too 1-dimensional from the perspective of it's “different for the sake of being different” as opposed to trying to convey some sort of design. Basically, you need more game mechanics and complexity for sure as was pointed out by LorenzoGatti.
I feel like the book mechanic is the most interesting thing design wise, that has potential to be improved upon and worked with, but I feel like there's no real inspiration or “soul” behind most of anything else. I see the basics of a working card game for sure, but I don't see the “imagination” behind using this theme of powerful wizards battling. I know this is an early draft, but I just feel like you need to be showing more personality behind what you're presenting.
I can't really tell you what I think you should do for your game, but I really think you need to start thinking about more thematic things and designing around those. I'll close by saying consider the following:
“I want to be a fire wizard that builds up burning effects on my opponent, which amplifies the damage my fire spells do”
“I want to be a hexxing wizard that uses powerful debuffs to render the opponent ineffective”
“I want to be a wizard that specializes in reflecting spells cast at me and absorbing spells to manipulate the damage done to mitigate them”
On one last side note, if you like HS and MTG, I highly recommend spending some time playing Legends of Runeterra. That game has some really interesting solutions to problems HS and MtG have, and I've been loving it. I'm not even into the LoL IP, but if you're looking for new inspirations, check it out.