I think I'm close to the end, but I've run out of ideas.
Partial answer
First lesson: the 12 concepts
The right edge of each card explains how to find a "concept" in another card:
Card: The Fool
Hint: The fool hides the protector (The Emperor)
Explanation: Like in a cryptic clue, the word is hidden in a phrase, "haj. Up, it erred"
Solution: JUPITER
Card: The Magus
Hint: Examine the sinister side of the Magus (The High Priestess)
Explanation: "sinister" means "left", we need to read the first letter of each line
Solution: SATURN
Card: The High Priestess
Hint: What does the dexter of the high priestess conceal? (The Lovers)
Explanation: "dexter" means "right", we need to read the last letter of each line
Solution: NEPTUNE
Card: The Empress
Hint: The Empress would reside and rule from the capital. Perhaps, these capitals are important (The Hermit)
Explanation: We need to read the capitalised letters
Solution: MERCURY
Card: The Emperor
Hint: Look literally and vertically at the heart of the emperor to find the city (The Hierophant)
Explanation: We need to read vertically from the "B" of the first line (the letter in the middle of the line)
Solution: BYZANTIUM
Card: The Hierophant
Hint: Are the numbers of the hierophant only numbers ? (Strength)
Explanation: A1Z26 with 13 1 18 19
Solution: MARS
Card: The Lovers
Hint: Lovers face each other (The Magus)
Explanation: We need to read from the end
Solution: CHRYSOPOIEA
Card: The Chariot
Hint: It is the last part of the sentences of the chariot which are the most important (The Wheel of Fortune)
Explanation: Last letter of each sentence
Solution: COPPER
Card: Strength
Hint: One of One, Two of Two and so on... (The Chariot)
Explanation: First letter of the first word of the first entry, first letter of the second word of the second entry, and so on...
Solution: ADEPT
Card: The Hermit
Hint: The Hermit steps down in threes. His coordinates are 10.22.23 28.12.12
Explanation: I don't know for this one
Solution: URANUS
Card: The Wheel of Fortune
Hint: The number of the Wheel of Fortune points toward the letters that are important (Justice)
Explanation: The Wheel of Fortune is the 10th card, so we read every 10th letter
Solution: QUICKSILVER
Card: Justice
Hint: In justice, consequences are after the ... (The Fool)
Explanation: First letter of every word after "the"
Solution: CINNIBAR (but I think it's "cinnabar")
I don't know the method for The Hermit but I deduced the solution with "Ignore the 7th planet".
Second lesson: the 12 bearers
The left edge of each card is made of 2 elements. We need to find pairs which point to famous persons.
First element: Flying a kite made of 100-Dollar bills (Strength)
Second element: Founding Postmaster (Justice)
Person: Benjamin Franklin
Explanation: Benjamin Franklin is famous for his experiment with a kite and lightning, he is on the 100-Dollar bills, and he was the first Postmaster General.
First element: So twice five miles of fertile miles (Justice)
Second element: With walls and towers were girded round (The Chariot)
Person: Kublai Khan or Samuel Taylor Coleridge
Explanation: Kubla Khan, poem by Samuel Taylor Coleridge
First element: Gnome (Justice)
Second element: Helical (Strength)
Person: Michelangelo
Explanation: Anagram
First element: The well-known HMS Galapagos (The Empress)
Second element: The famous Beagle Tortoise (The Hierophant)
Person: Charles Darwin
Explanation: Second voyage of HMS Beagle
First element: Qiantang (The Hierophant)
Second element: Year of the Goat, 1031 (The Fool)
Person: Shen Kuo
Explanation: Shen Kuo was born in Qiantang in 1031.
First element: Not the son or the father of Francis the First (The Magus)
Second element: But his close friend (The Fool)
Person: Leonardo da Vinci
Explanation: Leonardo da Vinci was a close friend of Francis the First.
First element: Islamic author (The Magus)
Second element: Kitab al-Manazir (The High Priestess)
Person: Ibn al-Haytham
Explanation: Islamic author of the Kitab al-Manazir.
First element: The day after Valentine's Day (The High Priestess)
Second element: The year of birth of the bard (The Wheel of Fortune)
Person: Galileo Galilei
Explanation: Galileo Galilei was born on the 15th of February (the day after Valentine's Day) of 1564 (The year of birth of Shakespeare).
First element: XVIIM (The Wheel of Fortune)
Second element: DCCLVI (The Hermit)
Person: Nikola Tesla
Explanation: Thanks to @fljx in the comments. XVIIMDCCCLVI can be interpreted as 10/7/1856, which is the birth date of Nikola Tesla.
First element: Ramo (The Hermit)
Second element: Mayyahk (The Lovers)
Person: Omar Khayyam
Explanation: Ramo Khayyam flipped
First element: Cobalt & Sulfur & Phosphorus (The Lovers)
Second element: Erbium & Nickel & Copper (The Emperor)
Person: Nicolaus Copernicus
Explanation: Thanks to @fljx in the comments. The symbols of the elements are Co, S, P, Er, Ni and Cu. We can rearrange them to Copernicus.
First element: 52° 48' 35.51" (The Emperor)
Second element: 0° 37' 42.57" (The Empress)
Person: Isaac Newton
Explanation: Coordinates of the birthplace of Isaac Newton
Third lesson: the precepts
According to the card "Enlightenment may follow", we need to answer 7 questions:
What is our private name for members of the order?
What is the first lesson a novitiate must learn?
What star guides our thinking?
Where is the foundation stone of the order?
Can you begin to employ the forces you wish to control?
Are you worthy?
How do you determine what the cards say?
The bottom of the three "statuette" cards indicates cards:
"Ignore the 7th planet" (A statuette of an owl) $\Rightarrow$ We need to ignore Uranus: The Hermit
"No space program" (A statuette of a raven) $\Rightarrow$ We need to ignore Mercury: The Empress
"Toss Scorpio" (A statuette of an elephant) $\Rightarrow$ We need to ignore The Chariot
If we take the letter at the bottom-right of the remaining cards, we have :
TFSOEFSXB
If we take "the letter before" as indicated by the bottom of the card "The enlightenment may follow", we have :
SERNDERWA
which is an anagram of WANDERERS.
I think it is the answer of "What is our private name for members of the order?".
Now, we can use the "statuette" cards. Each statuette indicates 6 pairs, and we can use the letters and symbols at the top of the cards to find three substitution cyphers.
A statuette of an owl
Hint: They lead together
Explanation: We need leaders
Solution: The Emperor and The Empress
Hint: The Vitruvian Man
Explanation: The Vitruvian Man was made by Leonardo Da Vinci
Solution: The Fool and The Magus
Hint: Rapidly changing father of Chronos from the first lesson
Explanation: "First lesson" indicates the concepts. "Rapidly" = "Quickly" and "Changing" = "Silver", so "Quicksilver". The father of Chronos is Uranus.
Solution: The Wheel of Fortune and The Hermit
Hint: The powerful arm of the law
Explanation: "Power" = "Strength" and "Arm of the law" = "Justice"
Solution: Strength and Justice
Hint: Servants of the church
Explanation: We need religious people
Solution: The High Priestess and The Hierophant
Hint: The vehicle of Cupid
Explanation: A chariot is a vehicle and Cupid is the Greek god of love
Solution: The Chariot and the Lovers
We now have the blue substitution cypher:
A statuette of a raven
Hint: PI
Explanation: $\pi \simeq 3.1$ so 3 and 1
Solution: The Emperor and The Magus
Hint: Circle of Life, both good and bad
Explanation: I don't really know
Solution: The High Priestess and The Wheel of Fortune
Hint: Emperor's New Clothes
Explanation: In the tale, the emperor is fooled.
Solution: The Emperor and The Fool
Hint: Ludovico Buonarroti
Explanation: Michelangelo di Lodovico Buonarroti Simoni is the full name of Michelangelo
Solution: The Chariot and Strength
Hint: The author of the Rubaiyat
Explanation: Omar Khayyam wrote the Rubaiyat
Solution: The Hermit and The Lovers
Hint: Biblical Law?
Explanation: "Law" = "Justice" and "Biblical" = "The Hierophant"?
Solution: Justice and the Hierophant
We now have the red substitution cypher :
A statuette of an elephant
Hint: Non-tropical Earth Signs
Explanation: Taurus, Virgo and Capricorn are Earth astrological signs and there is the Tropic of Capricorn, so we need the cards associated with Taurus and Virgo.
Solution: The Magus and The Hierophant
Hint: Fibonacci's first and fourth
Explanation: The first and fourth numbers of the Fibonacci sequence are 0 and 2.
Solution: The Fool and The High Priestess
Hint: Helium and Lithium
Explanation: Helium and Lithium are chemical elements like Cobalt, Sulfur, Phosphorus, Erbium, Nickel and Copper
Solution: The Emperor and The Lovers
Hint: Betting on the races
Explanation: A chariot is used for races, and a bet needs fortune (luck).
Solution: The Chariot and The Wheel of Fortune
Hint: Light minutes to the sun with the muses
Explanation: The light spends 8 minutes to go from the Sun to the Earth and there is 9 Muses. So we need the 8th card and the 9th card.
Solution: Strength and The Hermit
Hint: Astrology from Princess Ceca
Explanation: "Princess Ceca" is an anagram of "Pisces Cancer". So we need the card associated with Pisces and Cancer
Solution: Justice and The Empress
We now have the green substitution cypher :
We now can decipher the words at the bottom of the Major Arcana cards:
Green words:
CIENTSKY[B/W] (The Fool)
LIKETHEDI (The High Priestess)
VINENOMAD (The Hermit)
SOFTHEAN (The Wheel of Fortune)
Blue words:
WECLAIM[K/V]I (The Empress)
PLANETS (The Emperor)
NSHIPITHT (The Chariot)
HEANCIENT (Justice)
Red words:
EWAYSB (The Magus)
HSAREMA (The Hierophant)
NYALLTH (The Lovers)
ECOMEO (Strength)
I'm missing :
The explanation of The Hermit
The explanation for "Circle of Life, both good and bad" and "Biblical law?"
The answer of 6 questions
The fourth puzzle
How to continue the puzzle ?
With the coloured words, we can try to create sentences:
With the green words, we have LIKE THE DIVINE NOMAD OF THE ANCIENT SKY [W/B].
With the blue words, we have WE CLAIM KINSHIP ITH THE ANCIENT PLANETS.
With the red words, we have HS ARE MANY ALL THE WAYS BECOME O.
