1) Yes you are right. But the important thing is not that rich people can buy a lot of computers and mine a lot of coins. The important thing is that this does not make it impossible to mine the coins of all other people in the world! But now mining is available only to those who have a lot of money.
Your statement is partially wrong. While it's true that ASIC is quite expensive (compared with CPU), operational & maintenance costs plays bigger factor in this case.
Rich people still have advantage of cheaper electricity/cooling price on bigger scale.
2) No. CPUs are being monopolized ALREADY. Moreover, a long time ago - long before the birth of Bitcoin.
It is much more important here that mining will no longer take away the lion's share of all produced electricity from the whole world.
It is much more important here that mining will no longer take away the lion's share of all produced electricity from the whole world.
I don't see how CPU mining would prevent mining industry from taking lion's share of all produced electricity from the whole world.
3) You are mistaken ... 
Look at what scheme a regular pool works:
Here, ordinary users are forced to look for a Hash in the WHOLE range of nonce values. And users who are connected to the pool search only in the selected segment. Hence the gain in the speed of finding a suitable hash and a greater total reward.
And now see how the pool will work if the POW algorithm is based on my algorithm:
Are you see? Ordinary users search EXACTLY in the same range of values as users who are connected to the pool.
So - there will be no gain from pool.
Look at what scheme a regular pool works:
Here, ordinary users are forced to look for a Hash in the WHOLE range of nonce values. And users who are connected to the pool search only in the selected segment. Hence the gain in the speed of finding a suitable hash and a greater total reward.
And now see how the pool will work if the POW algorithm is based on my algorithm:
Are you see? Ordinary users search EXACTLY in the same range of values as users who are connected to the pool.
So - there will be no gain from pool.
Based on your image, pool miners look for different value range, which means parallelization is still possible and there's gain from joining mining pool.
If it's wrong, then the image illustration is wrong.