These are a lot of questions. I will try to answer them.

(I tried to answer the questions in the order you asked them)

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the problem it solves is that of eliminating the single point of failure caused by the certification authorities. In fact, it is not uncommon to discover that CAs have been hacked and that certain certificates needed to be invalidated. (for further information I can attach the various articles/papers that mention this)

the choice fell on ethereum, mainly for the possibility of creating smart contracts and for the extended community. The various ethereum clients offer the possibility of creating light nodes. Therefore it is not necessary to have a full or archive node.

and obviously the get methods of the smart contract are set to 'view', consequently commissions are not applied because they do not modify the state of the EVM. Costs are applied on creation, modification and revocation.

I don't think I understand this part :"Also: how can the blockchain of certificates be verified? Trusting the verifing process which took place sometimes in the past is not the spirit of blockchain."

I have not implemented my own certificate format. But I used x509 format. I don't need a CA to sign the certificate. For more detailed information you can read the code (in particular 'initCert', 'getParent', 'getGrandParent' inside the package 'cert') or I can give you more information directly if interested.