I agree with those point. However I don't see the issues being fixed that soon.
As for the last it takes a lot of man power to actually do the checking without a public id database.
I think you haven't understood how it will be done. It won't be manual labour (and no there isn't a public database).
The ID card has a chip that's even capable of digital signing, that's how the id can be automatically verified. They insert the card in a reader and identify themselves to the website or application in question. It's been explained already, and it's on the website's FAQ.
There is no paperwork involved on our partIs the type of card mandatory for every citizen in Spain ? There were users (from Spain) who claimed that not all Spaniards have one.
Is is free or legal , and can everybody have access to the verification mechanism?
Every citizen has a DNI (national identity document). Since 2006 they all have the chip-card. Some people have the old DNI but most have the new DNI-e, because there was a strong campaign to increase adoption. It's cumbersome to use on government websites though so people don't use it much, but its capabilities are there for anyone to use. DNIs have to be renewed every 10 years and we're on year 8 since dnie was introduced: that plus the initial campaign to boost adoption means practically everyone has it by now.
A USB iso7816 smartcard reader will do. Some keyboards have one built-in.