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Mining pools are a large node.
I disagree. I expect pools have few nodes across different region for various reasons such as ensuring faster block propagation.
Will such centralized computing power affect the security of Bitcoin?
There are some concern about centralization of mining hashrate. But almost all them are not economically feasible.
Can several large mining pools jointly launch 51% computing power attacks
It's theoretically possible. But their pool would be abandoned by miners and face possibility of legal sue due after attempting 51% attack.
Limiting computational power can also filter non mining nodes. Is there a problem?
Yes, because then only miners will be able to verify data. If you ban all nodes that are not mining, then you will have only miners in the network, and then the whole P2P concept is gone, because all other users will then be entirely banned, and would need to connect to the network by using some miner as a proxy.
Suppose I created a fake coin using Bitcoin running code, but I added two restrictions to this fake coin. Each user can only have one account, and the computing power of each account is limited to 100M. This fake coin has 1000 users. If someone tries to attack with 1T computing power, is the network still safe?
Bitcoin network would be safe / not affected since your modification break isn't compatible with current Bitcoin protocol/consensus. Other node would just put you into ban.
If we limit the number of registered users, will this system be fairer and more energy efficient than the current Bitcoin system.