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As per Karma theory, certain events of my current life are the fruits of my actions in one or more earlier births. Whose action's fruits am I facing in this birth? Given that it cannot be my current body or mind, it follows that it has to be my Atman. But according to Advaita, only Brahman exists and everything else is the product of Maya. In particular, the seemingly different people we see are all Brahman and seem different only because of Maya. Then how is it possible to determine the me from a previous birth? If one can indeed determine the me from the previous birth then does that not directly imply duality contradicting Advaita?

In fact I do not see how rebirth is even possible in the context of Advaita. Who is getting reborn? There is only Atman which manifests as duality through Maya. One cannot point to someone and say "you will be a great scholar in your next birth". For the statement to be true automatically means duality.

Advaita is true only in the paramarthika stage. We normally are mistaken by the world 'Jagat mithya'. The word 'Jagat' literally means something which is ever-changing.It comes from the root 'gam' which means movement. 'Mithya' here just does NOT mean false. It means :that which is not eternal or is ever-existing'. (Reference : Vivekanander Vedanta-Chinta, Dinesh Chandra Bhattacharya, RMIC).

We get both pleasure and pain because we are deluded by Maya. To cross the ocean of Maya, we need Brahma-Jnana or the knowledge of the never changing eternal truth Which is one with our True Self.To attain that knowledge, we first need'Chitta-suddhi' according to Sri Adi Sankaracharya.For Chitta-Suddhi, we need 'Nishkama-Karma' and 'Ishwara-Upasana'.So long as one has the sense of 'I' and 'My', he has to go on doing good works prescribed by the holy scriptures. So karma is essential to realise 'Advaita' in life.(Reference: Jnani-Guru, Paramahansa Nigamananda Saraswati, Sarasvata Math).

So long as we are ignorant of our True Self, we are Jivatmas. We have basically three bodies- Gross or Sthula,Subtle or Sukshma and Karana or Causal. The subtle body comprises of subtle karmendriyas and subtle jnanendriyas and manas. The causal body is caused by the ignorance that identifies the Self with these gross and subtle bodies. It is the causal body and the subtle body which together are together called Jivatma.This Jivatma dies and is born again and again so long as the true knowledge of the real Self is not obtained. The knowledge of the self destroys the mind which is root of all our ignorance. Being one with our True Self ends our endless journey between births and deaths.

Yes, rebirth is true in duality.When Maya is gone, duality is gone and there is neither birth nor death.

So rebirth and Karma are fully consistent with Advaita (Reference:Jnani-Guru, Paramahansa Nigamananda,Sarasvata Math).

As per Karma theory, certain events of my current life are the fruits of my actions in one or more earlier births.

Yes

Whose action's fruits am I facing in this birth?

Your own.

Given that it cannot be my current body or mind, it follows that it has to be my Atman.

By this reasoning you are saying you are not responsible for anything you did yesterday or anything before current moment.

In particular, the seemingly different people we see are all Brahman and seem different only because of Maya. Then how is it possible to determine the me from a previous birth?

If you can identify yourself as doer of a task among many people, you performed yesterday, then you may very well also identity yourself among many people of your previous birth tasks.

If one can indeed determine the me from the previous birth then does that not directly imply duality contradicting Advaita?

This contradiction seems to even arises if you think you can identify yourself as doer of a task you performed yesterday among many. Because according to Advaita, only one exists. Even in this every moment this contradiction arises. You may simple say, if Advaita is true, why are there so many people.

In fact I do not see how rebirth is even possible in the context of Advaita. Who is getting reborn?

Again, I really do not see your argument here. What's the problem with rebirth? It's just like going from yesterday to today or childhood to youth to old age. If you take yourself as the same person yesterday and today, what is wrong with rebirth? Like Krishna says:

देहिनोऽस्मिन्यथा देहे कौमारं यौवनं जरा।

तथा देहान्तरप्राप्तिर्धीरस्तत्र न मुह्यति।।2.13।।