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Third, Churchill's orders regarding the two ships were obviously issued LONG before Pearl Harbor. The ships left England weeks before Pearl Harbor and Churchill's control ended then.So situation changed and they went ahead as Pearl Harbor was still smoking - DUMB.Irrelevant when they left or orders were issued there was now a clear and present danger.With a whole Island pummeled two ships would be target pratice

Fourth, Repulse and POW were not sent without air cover. They were sent with a carrier but it suffered damage and had to stop for repairs.So no air power in other words - DUMB.And still forged ahead

Fifth, Churchill would reasonably have assumed that Repulse and POW could operate under air cover provided from Singapore and other British bases in the region. And what happens when someone ASSUMES?

Sixth, in hindsight it was obviously ludicrous to send Repulse and POW beyond their air cover but that wasn't realized until after they met their demise. At Pearl Harbor and at Taranto before that IJN and RN planes had sunk and damaged heavy ships but a lot of people still thought that was because the ships were caught by surprise and unable to maneuver. The above statements are not hindsight that should be was an obvious blunder not factoring in the reasults of just 3 days earlier.Japan had at least 18 carriers at that time and w/o knowing their location well that was just DUMB

• This is CLEARLY well below the level of a decision that the Prime Minister would be responsible for.  
• You are asking for an impossible level of speedy change in military doctrine.  This is like saying that the French should have adapted to the Blitzkreig tactics while the Battle of France was ongoing.  Sure, they *SHOULD* have, but they didn't.  Why?  Because it takes more than 30 seconds to completely rearrange a military doctrine that has been enshrined for decades and taught to every level of officer.  These things can't be changed instantaneously because you can't go back in time and retroactively retrain your entire officer corps with the new doctrine.  
• The actual level of destruction at Pearl Harbor wouldn't necessarily have been clear to even the American let alone the British high command within the three days.  There is literally no chance of any military in the history of militaries being able to learn the lessons of Pearl Harbor and then completely change their doctrines based on those lessons in 72 hours.  To suggest otherwise is absurd.  
• The whole island wasn't pummeled.  On the contrary, much debate in the eight decades since Pearl Harbor has focused on Nagumo's decision NOT to send the third wave which would have attacked the base facilities.  The attack sank or damaged a number of ships and destroyed a vast number of US Aircraft (mostly on the ground) but did almost no damage AT ALL to the base facilities.  Pearl Harbor was able to continue to function as an effective fleet base because their drydocks, ship repair facilities, oil storage tanks, and sundry were almost completely unscathed in the attack.  This is to say nothing of the radar installations, shore artillery, and other land-based items that were not even intended targets of the planned third wave.  

• To the extent that this criticism is even arguably valid, it is a criticism of the Captains and Admirals in charge locally.  It doesn't even rise to the level of the First Lord of the Admiralty (British equivalent of our Secretary of the Navy) let alone the Prime Minister (British equivalent of our President).  It is patently absurd to think that FDR or Churchill should have been making local tactical decisions about ships literally thousands of miles away.  
• Even there, the criticism still isn't valid as applied to sending the ships to Singapore.  Singapore was NOT bombed by the Japanese in force until much later.  They couldn't do that in force until they had captured airbases in Malaya.  Repulse and POW were sent out from Singapore to interfere with the Japanese landings in Malaya.  THAT decision is the one that was questionable at the time and ludicrous in retrospect but the order to send Repulse and POW out of Singapore specifically to impede the Japanese invasion of Malaya was made IN Singapore, not at Downing Street.  
• As stated previously, Repulse and POW were the first Capital Ships to EVER be sunk by air power alone while having freedom of movement.  The Italian and American Capital Ships sunk at Taranto and Pearl Harbor were stuck in their harbors and unable to move (takes time to build up steam).  It wasn't just Churchill nor even just the British who failed to grasp that this was a very real possibility.  A substantial portion of the world's admirals were still clinging to the idea of Battleship supremacy between December 7, 1941 (Pearl Harbor) and December December 10, 1941 (sinking of Repulse and POW).  What you are missing here is that, to the world's admirals and Naval Staffs the sinkings of Repulse and POW were far more shocking than the sinkings at Taranto and Pearl Harbor.  Unfortunately for the British the sinking of Repulse and POW *WAS* the lesson, not the result of a failure to learn from the earlier lessons (Taranto/PH).  

• Again, not the Prime Minister's nor even the First Lord of the Admiralty's job to determine and dictate local tactical decisions.  If you want to say somebody was stupid and that stupidity caused the loss of Repulse and POW that is fine but your insistence of directing this criticism at Prime Minister Churchill is bizarre.  It would be like if you had a Cadillac with some defect and rather than blaming the dealer or the factory QC, or the factory line worker who screwed up, or the foreman of that unit, or the superintendent of that line, or the executive in charge of that factory, or the executive in charge of Cadillac, or the CEO of GM you instead decided to skip all of those people and assign blame to the Chairman of the Board of Directors of General Motors.  

• Ah, this sentence would be a lot easier to address if it was actually a property constructed sentence but I *THINK* I can divine your meaning.  
• Here you bring up the 3 days thing again as if it favors your apparent argument that Churchill was an idiot.  No, it doesn't.  It is apparent that Churchill himself issued NO orders regarding Repulse and POW between learning about PH and the loss of Repulse and POW so the short time undermines rather than supports your argument.  
• In addition to that, the three days is misleading.  By the time the PH attack was learned about in London it would have been the next day at least and they probably didn't truly know the extent of the damage until AFTER Repulse and POW were lost so the idea that anyone in London let alone the PM should have gotten a report about PH, figured out that it meant that Capital Ships were vulnerable to air attacks even when possessing freedom of maneuver (not the case at PH), and then issued an order to not send Repulse and POW out is ludicrous.  However, even if we ignore ALL of that, it wasn't remotely within the province of the head of the British Government. That is a tactical level doctrine issue that at the highest should have been dealt with by the First Lord of the Admiralty.  
• Japan NEVER had 18 "true" carriers.  At the time of PH they had six fleet carriers and on December 10, 1941 all six of them were on their way home from Hawaii and/or dealing with the American defenders on Wake Island.  I seriously doubt the assertion that Japan had "at least 18 carriers" but I absolutely KNOW that they only had six fleet carriers.  Other carriers that they did have were light carriers, escort carriers, and seaplane carriers and none of those are particularly relevant to the discussion.  Actually carriers are irrelevant to the whole question since Repulse and POW were NOT sunk by carrier-based aircraft.  They were sunk by land-based aircraft only AFTER they ventured into range of such planes and out of range* of their own air cover.