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No, every node executes the code running on the blockchain. This will be changed with sharding requiring only a percentage of nodes to run the code.

Not sure where that's from but that's not true. There are no intentional inefficiencies and you can't mine Ethereum individually.

You can mine with you GPU in a pool. You can earn a whopping $4 a week with a mid range GPU.

I wasn't saying that it's intentionally inefficient, just that it's purposefully designed to be ASIC unfriendly.

Ethereum hashing algorithm is optimized to be ASIC resistant, in other words you can mine it with GPU and CPU, a more accessible kind of hardware (in fact home hardware).

That's not an inefficiency, it's if anything more efficient with GPU.

The transaction problem applies to both, regardless of the mining algorithm.