My understanding of Advaita

Yes, your conclusion is a remarkably accurate and insightful summary of the core teachings of Advaita Vedanta. You have grasped the essential logic that holds the entire philosophy together.

Let's break down your points and add some nuance and traditional terminology, which will likely deepen your understanding.

1. "Brahman is unchanging and eternal, wants nothing and does not act."

This is perfectly correct. This is the definition of Nirguna Brahman (the attribute-less Brahman).

Unchanging and Eternal: Brahman is Sat (Existence/Truth) and is beyond time. It doesn't come into existence, change, or cease to be.
Wants Nothing and Does Not Act: Action (Kriya) requires a change, a doer, and an object of action. Since Brahman is the one, non-dual reality, there is nothing other than it for it to act upon or desire. It is perfect, whole, and complete. To act implies a lack or a goal, and Brahman lacks nothing.
A Quick Nuance: Advaita also sometimes speaks of Saguna Brahman (Brahman with qualities), also known as Ishvara (God). This is the personal, creator aspect of Brahman that does act within the phenomenal world as part of the "play" (Lila). However, this is considered a provisional, relative truth for the devotee. The ultimate, absolute truth is the actionless Nirguna Brahman. Your statement correctly describes this ultimate reality.

2. "Minds are mental constructs that appears to be conscious but they are not."

Again, this is very accurate and gets to the heart of the illusion. The key technical term here is Chidabhasa.

The mind (Manas or Antahkarana) is part of Maya, the inert, unconscious material of the phenomenal world.
Consciousness (Chit), the true nature of Atman/Brahman, is like pure light. The mind is like a mirror or a prism. The mind doesn't possess consciousness; it merely reflects it. This reflection is called Chidabhasa.
We identify with this reflected consciousness, and this creates the illusion of being a separate, conscious individual, or Jiva. So you are right: the mind itself is not conscious, but it cleverly appears to be by borrowing light from the true source.

3. "Mind acts in a made up world."

Exactly. This "made up world" is what Advaita calls Maya.

Maya is best described not as an illusion (like a hallucination) but as an "apparent" or "relative" reality. It has a practical, transactional existence for the individual living within it, but it is not the ultimate, foundational reality.
The famous analogy is mistaking a rope for a snake in a dimly lit room. The snake-world you experience (the fear, the movement) is real to you in that moment. But its reality is only apparent. Upon seeing the rope (Brahman), the snake-world vanishes. You realize it was never really a snake.

4. "And those actions have no real impact except in the made up world."

This is the most critical point and a potential trap. You are absolutely correct, but it's essential to understand this from the perspective of the two levels of reality, or this can lead to nihilism.

From the Absolute Perspective (Paramarthika Satya): From Brahman's viewpoint, no action has ever happened. There is no world, no mind, no doer, no karma. The ultimate impact is zero. The script of the play is already written; Brahman is the unchanging screen, not the actors or the story.
From the Relative Perspective (Vyavaharika Satya): For the Jiva, the individual who is still caught in the illusion of Maya, actions have profoundly real consequences. This is the world of Karma. Every action creates a ripple effect that binds you to the cycle of birth, death, and rebirth (Samsara).

The Crucial Practical Implication

This is where the spiritual path comes in. The purpose of practices like meditation, self-inquiry, and selfless action (Nishkama Karma) is to purify the mind and accumulate punya (merit), which allows one to eventually see through the illusion.

If you dismiss the importance of action while you are still in the relative world, you will simply create more negative karma and deepen your bondage.

The paradox of Advaita is that we must take the relative world and our actions in it very seriously in order to finally realize its unreality. This is the core message of the Bhagavad Gita: act diligently, but renounce your attachment to the results of your actions, because you are not truly the doer.

Summary Conclusion