you are in a heap of trouble if you leave and try to return. they will know. it all shows up. welcome to 1984
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US CBP and ICE generally do link a person's passport to their immigration files eventually. I recently defended a case where they linked the person's new passport several years later, found he was inadmissible for having an unlawful presence issue and we had to litigate whether or not he entered fraudulently with the new passport. Based on that experience and others, I'd recommend retaining counsel before you do anything to ensure your next attempted entry is proper.
These days they scan it (new Irish passports have chips in them) so the stamps really don't count for much. Believe me, the US knows everything about your visit. If you want to learn more about whether you are inadmissible because of past immigration violations, you should consult an immigration attorney.
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There is not enough information. Generally there will be at least some record of your departure from the U.S., at least from the flight manifest.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.
What additional info? I agree with my colleagues. Yes they know. It's a very big risk. It does not matter who stamped what. The stamps aren't the only proof.
Dhenu Savla, Esq.
This answer does not create an attorney-client relationship and is not meant to be relied upon as legal advice.