There is just no evidence that: 1) Atlantis even existed; 2) that, if it did, Atlantis was located somewhere in Western Europe; 3) that, if it existed somewhere in Western Europe, it was really very advanced, and not just comparably advanced for the standards of primitive civilizations; 4) that R1b as a whole (as opposed to some specific subclades of it) is strongly associated with red hair; 5) that R1b was present in any high frequency anywhere in Western Europe until the Bronze Age (until now AFAIK virtually no R1b of the modern clades of Europe, almost all of which derive from R1b-M269, appeared in any ancient West European DNA before ~2500 BC); 6) that the supposed R1b (was it confirmed really? I don't know) in Tutankhamen belonged to the same lineages found extensively in Western Europe; 7) that the rise of sea-levels was "virtually overnight", or rather the evidences are totally contrary to that, that it was a really rapid though varying process for geological standards, but still took many centuries to complete; 8) that King Tutankhamen and other New Kingdom pharaohs of Egypt belonged to the same royal lineages that were responsible for the first dynasties and the nascent civilization of Old Egypt.
In my opinion that hypothesis is based on very weak and arguable foundations.
Btw, the Tarim Basin mummies have nothing to do with the Han Chinese civilization that arose hundreds of kilometers to their east and started to expand from a completely different area and direction. They just lived in the modern territiory of the state called China and probably interacted occasionally with the ancestors of the Sinitic/Han civilization. That's it.
1. There is no proof, but there is certainly evidence (Plato's account corresponding exactly with geological data regarding the Younger Dryas Impact event, Greenland cataclysmic meteor/asteroid impact, end of the last Ice Age, huge near instantanious rise of sea-levels upto 400m which corroborate the global "flood myths"/deluge that is spoken about from Egypt, to China, to South America etc..., survivors of an advanced civilisation coming from the sea or skies (dependent on the myth/culture) bringing with them advanced culture and technology, architecture (megalithic structures, pyramids etc...)
2. Sure, this is all speculative, I am not trying to assert my opinions as fact, as you seem to be.
3. Sure, no one stated otherwise.
4. There is a high correlation to red-hair and R1b, if you don't want to believe the connection then you are of course welcome to do so.
5. You may be correct that there is little evidence right now, but there are R1b red-haired mummies found all over the globe, and then the highest modern day concentration is on the British Isles (pre-dominantly Ireland, Scotland, and Wales), the accumilation of it to the vast West would give some possibility of them having arrived from the West thus being concentrated there, rather than having traveled all the way East (which I am not denying happened) and not stopping until they reached Great Britain.
6. Discovery Channel documentary claims that 40% of British and European males share the same DNA as King Tutankhamun, yet only 1% of modern Egyptians share that same blood.
7. There is much evidence (most within the past year or two) to show that the Greenland impact at the end of the Younger Dryas caused near instantanious sea-level rises of upto 400m, corresponding perfectly with the date given by Plato for Atlantis' sinking, and also the global flood/deluge myths of countless cultures spanning the breadth of the globe. There is much evidence that even the huge canyons of America where carved out nearly instantly by huge 400m tidal waves with chunks of iceburgs still being carried, rather than the currently held theory of slow erosion over millions of years.
8. Until we find preserved remains of the first kings of pre-dynastic Egypt, one can neither prove or disprove it, the fact is though, that they in-bred to an extreme degree, indicating they were trying to preserve their bloodline for some reason, the most likely reason to me being that this was a very special and ancient blood-line, that differed vastly from any of the "native" Egyptians or peoples of that area.
In-regards to your statement that the Tarin Basin mummies have nothing to do with Ancient CHina because they were based "hundreds of kilometers to their east", I'm not sure what that is supposed to prove. Peoples of ancient cultures dragged megalithic blocks of 200-800 tons over 500km, so that sort of distance is extremely trivial and does not present any challenge in-terms of communication, or travel (for instance Roman soldiers marched 50 miles a day (80km), so even by foot it is only a few days walk, without the use of horses or other animals.