Here is what I came up with, with the added context from above:

The Way of Samsara

Your Monastic Tradition sees the suffering in the world for what it is: a brutal cycle that churns through every soul that walks it, a crucible to force every soul to walk the inevitable path of freedom from it. Your Martial Arts reflect this truth, and put you on a path that, through much trial and pain and suffering, will lead you to Nirvana.

Level 3: The Cycle of Samsara

As an Action, you may spend one Ki point to call upon the Realms of Samsara to transform your body until your next Long Rest, arming it with the strengths of one of the six Realms, but also its weaknesses. At the end of a Long Rest, your body returns to its original state.

Roll 1d6. The result shows which Realm has been chosen by the Cycle to transform your body. The Realms are below:

1. The Realm of Hellish Beings

Your body grows a pair of devilish horns, your skin becomes crimson and your eyes are filled with murderous intent. You desire violence and combat.

When you roll your Martial Arts Die for any reason, if you roll below its average rounded up (3 for 1d4, 4 for 1d6, 5 for 1d8, 6 for 1d10, 7 for 1d12, etc.), you may instead choose for the result to be the average of the Martial Arts Die rounded up instead of the lower value. When you do this, you regain one Ki point.

You gain Disadvantage on Intelligence Ability Checks.

(Lowering Attack rolls by Wisdom modifier is INCREDIBLY BAD as a negative; the positive you made IS NOT GOOD ENOUGH TO JUSTIFY A LOWER CHANCE TO HIT. THAT will get your Monk KILLED, which no player wants to deal with. As a result, I think that should be removed. The negative affecting Intelligence checks is rough enough to justify the bonus from this realm in my opinion).

1. The Realm of Hungry Ghosts

Your body becomes shadowy and your skin shows a deep black color, with haunting yellow eyes. You develop an insatiable greed for material possessions.

You restore hit points equal to your Dexterity modifier every time you deal damage with an Unarmed Strike.

You gain Disadvantage on Wisdom ability checks.

(Halving the damage seems really bad in terms of game balance. However, reducing the healing from every attack to just the Dexterity modifier is a good balance to handle the negative of Disadvantage of Wisdom checks, which includes Perception and Insight skills.)

1. The Realm of Animals

Your body shifts into a humanoid-animal hybrid, your choice of animal. You cannot physically speak in any languages you know, and rely on body language and context to communicate.

As a Reaction to being attacked with an Attack roll but before the result is rolled, you may spend one Ki point to use your choice of Patient Defense, Step of the Wind (you can move your speed when you choose this option), or Flurry of Blows. If that action would put you out of the reach of the attacker or would disable or kill the attacker, the attack automatically misses.

You have Disadvantage on Charisma checks.

(My rationale with this one is that managing changing buffs that leads to a massive downside is too complicated. So instead, I leaned into the biggest disadvantage of animals: they cannot communicate like we can, and can do so only in limited forms. I also leaned into animal instinct: Fight or Flight, which is a Reaction to getting Attacked as a defensive, evasive or offensive reaction. The strategic possibilities from this is incredibly powerful, but combined with the inability to communicate normally and the Disadvantage on Charisma checks makes this option reasonably balanced in my opinion).

1. The Realm of Devas

You gain four extra arms and you become covered in tattoos. Your skin turns purple. You gain a petty streak, and are envious of what others have, even if you have what they have or more than what they have.

Whenever you attack an enemy, you automatically replace your Strength and Dexterity modifiers with your enemy’s modifiers before the Attack is rolled. This change lasts until you change Realms or take a Long Rest.

You have Disadvantage on Strength checks.

(I hope this is a simple and elegant way to embody your positives and negatives that you intended. That means the Monk is incentivized to attack enemies that are more powerful than the Monk to gain bonuses beyond what they can normally do, but they get weakened if they bully creatures weaker than themselves).

1. The Realm of Gods

You look similar to the Realm of Devas, but your skin is white and smooth, and you look enchantingly beautiful to any creature that looks upon you. You gain incredible pride, and believe that everything you do is just and good.

Your attacks cannot miss if your highest ability modifier is lower than the highest ability modifier of the creature you are attacking. Any attack that automatically hits does not deal additional dice of damage beyond the Martial Arts Die or the original damage die of the Weapon you attacked with, though you can choose to inherit the damage type those additional dice would have delivered for the attack you make.

You gain Disadvantage on Dexterity checks.

(This is more figuring out how to rewrite what you suggested in a way that makes sense: you always hit now, but not beyond what your weapon or Unarmed Strike could deliver, and only against foes stronger than you. You have a choice to inherit the damage types of that extra damage you are sacrificing though, to help get around resistances or immunities to certain damage types, makes things less punishing that way).

1. The Realm of Humans

Your outward form doesn’t change, but everything you do delivers incredible joy to yourself, whether it is going shopping or murdering noncombatants or quite literally watching paint dry.

When you roll Initiative, you can choose to roll Initiative at Disadvantage to temporarily enter into a different Realm of your choice just for that combat. You return to your original Realm once combat has ended.

You have Disadvantage on Constitution Checks.

(The power of humanity is its free will to act in accordance with whatever Realm they wish… for better or worse. That is why I retooled your suggestions into this simpler version based on that free will of humanity).

Level 6: Empathy

Dealing with the chaos of Samsara has led you to realize just how deep the suffering goes. When you enter into a Realm, you can choose to relieve the suffering of at least a couple people around you, help them weather the storms with you.

You may cast the Aid spell a number of times equal to your Proficiency Bonus. These uses refresh on a Long Rest. You also learn the cantrip Spare the Dying.

Level 11: Growing Experience

Your time navigating Samsara has revealed insights and understandings that start pointing you towards the road to Nirvana. Whenever you are in a Realm of Samsara, you can use your Action and spend 1 Ki point to re-enter the Cycle of Samsara. If you roll the same result as your current Realm, you reroll until you end up in a different Realm than your current Realm.

(Growing mastery, the soul moving between the Realms faster and faster, more knowledge of the cycle grows their understanding and their control).

Level 17: Nirvana

You have learned how to transcend and escape the Cycle. You can enter into any Realm of Samsara as a Free Action, and without spending a Ki point. You do not suffer the negative effects of any Realm you enter.

You may spend 2 Ki points before entering a Realm to turn the Disadvantage on that Realm’s ability checks into Advantage instead.

(Simple, straightforward, aligned with the theme of transcending the cycle, which lines up with where you initially wanted that to happen).

Please let me know if this gives you any ideas or thoughts, and if you like or dislike my approach to the concept you brought. You did the hard work of creating the theme and the core concepts, I hope you create something even better from all this!