I think your paper thicknesses are off.
A ream of paper is generally 500 sheets and 2 to 2.5 inches thick. 25.4mm per inch 25.4 * 2.5 = 63.5 mm per ream. 63.5 / 500 = .127mm per sheet of not the thinnest paper. This calls into question the rest of the math...
It seems best to go directly to the dimensions from a notecard seller Amazon sells 3x5 note cards packaged in negligible plastic and measuring 0.8 inches thick. 0.8 * 25.4mm = 20.32mm per pack / 100 = .2032mm per card.
EDIT - Wording.
From left to right the subjects are Math 4 (basically the same as what most high schools call precalculus), AP Pyscology, AP European History, AP US History, and AP World History.
I don’t know how many notecards there are but I would guess over 1000.
Edit: According this Amazon product, 100 cards are 0.81 inches tall. All of these notecards stacked on top of each other is approximately 9.75 inches tall (with the rubber bands and after I push down on it a little. 9.75 / 0.81 * 100 ≈ 1204 cards. Because these are probably less densely packed than the package and also have rubber bands, let’s just say it’s 95% as dense as the package. 1204 * 0.95 ≈ 1144 cards. /r/TheyDidTheMath
I've seen that trick done with ruled index cards to plastidip wheels. Seems to work very well if you're careful!
https://smile.amazon.com/dp/B002OB49JQ/ref=cm_sw_r_cp_apa_fabc_CkQYFb94ZHDDZ
Cut it to size, put your info in it, and wrap it on the inside of the head tube around the fork. I haven't done it in a long time, but that's the gist of it.
Stop starting your sentences with "So." It makes everything you say sound weak and uncertain.
Good luck with your card game. I've made a few CCGs in my time as well. Your best bet for prototyping is to use common lined notecards. I used to get the 3x5 cards and cut them in half. These are cheap, quick to make, and if you need to change the rules or how a card works/written instructions on a card you don't have to worry about working around artwork. You could also use blank playing cards, but those are just more expensive and aside from being a bit more sturdy don't offer much else in the way of function.
Once you get the rules set down and working well, and get the game to the point where the gameplay is fun and interesting, then you can start worrying about artwork and how the cards actually will look in a "production" version of the game.
But for now I wouldn't worry about how the game looks, because regardless of how nice it looks no one is going to play the game if it is boring.
You can get them in packs of 100, too!